Biology
General
Easy
Question
When the solute has been added in the solution, then following observation can be made ?
- The DPD of the solution decreases
- The
w of the solution increases
- DPD of the solution decreases while its
w increases
- DPD of the solution increases while its
w decreases
The correct answer is: DPD of the solution increases while its
w decreases
Related Questions to study
chemistry-
B can be obtained from halide by van Arkel method. This involves reaction
B can be obtained from halide by van Arkel method. This involves reaction
chemistry-General
Maths-
If
then
=
If
then
=
Maths-General
maths-
=
=
maths-General
chemistry-
Element Element M belonging to group 13 can be
Element Element M belonging to group 13 can be
chemistry-General
maths-
In
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In
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maths-General
maths-
In the given figure, ABCD is a Parallelogram then ar (
AFB) is
![](data:image/png;base64,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)
In the given figure, ABCD is a Parallelogram then ar (
AFB) is
![](data:image/png;base64,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)
maths-General
maths-
In the following figure, if
ABC is circumscribed over the circle, then x =
![](data:image/png;base64,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)
In the following figure, if
ABC is circumscribed over the circle, then x =
![](data:image/png;base64,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)
maths-General
maths-
ABC is an Isosceles Triangle inscribed in a Circle such that AB = AC = 17 cm, BC = 16 cm then radius of Circle =
![](data:image/png;base64,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)
ABC is an Isosceles Triangle inscribed in a Circle such that AB = AC = 17 cm, BC = 16 cm then radius of Circle =
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMYAAAC8CAYAAAAjItH6AAAgAElEQVR4nOy9Z3NbV5a/+yAnAiBAEsw5gzmLlERRluXQst3tcU2n+++aeTcfYT7EfIVbdev/pnvG093qbgc5yQqUGMWcQDBnkAQJEgCRgXNfyERLtmyLEklANp4ySrJInLOBc35nr7X22muJBEEQSJAgwVOIYz2ABAnikYQwEiR4BglhJEjwDBLCSJDgGSSEkSDBM0gII0GCZ5AQRowQIhEgESmPV6SxHsDPjwjOzTV2FjfwG9PQlZWSIgV1rIeV4CkSwjhXBMDO9tR97n80zG5hM6X6fNqy5KhFsR5bgidJCONc8cGRlW3rHR50D2FdUdNR46JEm0KOLtZjS/AkCR/jHBFCXvwrCzht8xwKeyysbzI2sMz6ToBIrAeX4CkSwjhH/M4j1qbdBEIaShuzSNW42BobYW51m/1YDy7BUySEcS4IgIMj5ybT63I8uibaulq4lO9HsTSA1bqG1Q3+WA8zQZSEMM6FMPgXce0tsSJKxV/8GlWNnbxVqqQ8Msu6dYlHiwKOQKzHmeCYhDDOg3CY0NIKztUNAqZMFPUXyCm7wuWqHJqynThWZhkaW2PHHYr1SBN8Q0IYZ44AYRe7czZWZ2yEggcEIi7WtwP45BqSUsX4NmZZHBpj0e5NmFNxQiJce+b4CAU3WbI7sSw7cQcnkcqO6BcFSXL62JEkIdlfxWMdZXqjkYpSLeUiSCxrxJbEjHHWhPaI2BfYFiXhzGggO91EoVKMWiZFklFLbk0rrdkhUpyTTM5uMb2TEEU8kJgxzgwBhAjhVSubE1NsB/NQNnZSW5WEOVVMRACRGLzrBpKXH+HonWdmYIShvFwuvpZGmkKMOKGQmJEQxlkR8RCwzzNz/yvufz3KULKCzBtalJkpJCf989eSjzSkaiMEd6ewrP2VsFRJqaGLS+ZM8vVSZLH7BD9rEqbUWSEECXt22T3wselJQiSSYJQ6ISw8scrtwx8UIUmvIKekgoqUEGqfjfUdJwcBgXAMh/9zR5SoEnJGCH5CLhsbi2us2XwEtSZSC/PJTNVilIu/eSIFCbl22d9cZWV1G5tLRFiXRWZBAflZRlLV4sSUHiMSwkiQ4BkkTKkECZ5BQhgJEjyDhDASJHgGCWEkSPAMEsJIkOAZJISRIMEzSAgjQYJnkBBGggTPICGMBAmeQSLj4CUJBAJ4PB78fj/BYJBAIPDUn6FQiEgkQjgcJhgM4vf7iUQeZ0sJgoBEIkEulyOXy5FIJIjFYqRSKTKZDJlMhlwuj/6pUChQqVQoFIoYf+qfPglhvAQOh4ONjQ3W19fZ3d3l4ODgqdfh4SEulwu/308gECAUerx1VSqVIhaLCYfDT/2bXC5HqVSi0WjQ6/UYDAaSk5PR6/UYjUZSUlLIzs4mNzcXo9EYy4/+kyeRK/WcbG1tYbPZ2N7e5vDwkMPDQ5xOJ0dHR3i9Xnw+X3RGCAQC0T+DwSDhcJhIJEIkEiEYDLKyssLm5iaZmZmUl5cjEokIh8NIJBKkUilSqRSFQhGdSZ58PUs4aWlpZGZmkpGRgVicsI5Pg4Qwvofjm9jv97O6usr09DQzMzPMzs6ytbWF0+lEpVJhMpnIzs7GaDSSnJxMUlISOp0OnU6HVqtFqVSiUChQKBT4/X6Wl5f5n//5H3p7e7l8+TL/8R//gdFojM4ewWAQr9eL2+2Ois/lcuFwONjb22NjY4OtrS38fj8Gg4GMjAxKSkowm81UVVWRn5+PSqVCKpUikUhi/TW+siRMqWewv7+PxWJhbGyM1dVV9vf3CYVCiMVitFotycnJKJVKDAYDaWlpZGRkYDAY0Ol0JCUlodVq0Wq1aDSa7xx7e3sbj8eDSCRCJpNhMBgoLy//zu95PB5cLhdOpzMqEofDEZ21HA5HdJZaW1tjdXWVr7/+mpSUFHJzc6mpqaGqqorU1NTz+Mp+ciSE8Q3HN6HNZmNxcRGLxcL4+Dibm5solUpKS0sxm81UVlaSl5eHyWRCo9EgFosRiURPvb6P5eVlbt26RW9vL263m5GREW7evMlvf/tbCgsLn/pdtVqNWq0mPT0dQRCeekUiEdxuN5ubm6yurjI7O8vU1BQLCwtMT0+Tnp7Ozs4ONpuNoqIiMjMzo7NZgucjYUoBdrudwcFB+vv7mZmZIRgMYjKZyMrKIiUlhfT09Kdeer3+xOcIBoPcu3eP//qv/+KLL75AJBKh0Whob2/nP//zP7l27dqJjykIAg6Hg93dXba3t6Ovvb09dnd32draQiwWYzabuXTpEk1NTQmn/Tn52c4YPp+PxcVFFhYWWFpaYnFxka2tLXw+HxkZGdTX19Pe3k5paSlq9ct3r1heXmZiYoJwOIzRaIyaSOvr6ywsLNDU1IROpzuR8ywSiTAajRiNxqg5dnR0xMLCAkNDQwwMDLC+vo7FYsHlcmGxWCgpKaG4uJjCwkJkssSO8u/jZykMj8fD5OQkn3/+OX19fbjdbnJzc7lw4QI1NTXk5OREQ6SnsWbg9/sZHBxkYmKCvLw8JBIJQ0NDBAIBDAYDCwsLjIyM0NLS8tLmjkajoaKigoyMDDo6OlhbW2NycpL+/n4GBgYwGo10dnby+uuvYzabkcvlL/35for8rITh8/kYGxujr6+PyclJ9vf30ev1mM1mqquraWlpwWw2n/p59/f36e/vZ35+nnfffZf8/HyWl5fR6XRUV1eztLTEnTt3KC0tPRU/QC6XYzKZMJlMlJeXk52djVarZWpqio2NDQYGBpifn8dsNtPa2kpDQ0Ni0fBb/CyEEQwGcTgcjI+Pc+/ePXp6egiHw7S0tPDWW29RXV2NXq8/k6en3+9ndnaWpaUlpFIpFRUVOBwOtFotZrOZpqYmPv74Y0ZHR1lbWyMrK+vU1yLKy8spKCjg8PCQ4eFhvvjiCwYHB7FYLNhsNlwuFzU1NRiNxsQM8g0/C2FMTU3xySefMDQ0hEgkorKykurqaurr66murj7TaM3y8jL9/f34fD6qqqooLi5mamoKiURCdnY21dXVDAwMMD09zdTUFAUFBWRkZPxgdOukiMViVCoVKpWKjo4OdDodRUVFjI2NMTo6yuTkJE1NTbz99tu0trae2nlfZX7Swtje3mZ8fJz79+8zODhIJBLhwoULvP322zQ1NZ3L03F8fJwHDx6g1Wp54403yMrKYnh4mHA4jEKhIDc3l7a2tqiJk5ubS3p6+qkK40mSk5O5dOkSjY2N9PX18dlnn9Hf38/du3dxuVzs7+9TV1dHZmbmmZz/VeEnK4ytrS3u3LnDRx99xPb2NtXV1XR1dVFdXU1OTs65iMLhcDA9Pc3i4iJXrlyhra0NnU4XTS4MBAIkJyfT3t7O8PAwExMTFBQUcOnSpWcuDp4marWalpYWMjMzqauro7u7m56eHhYXF3nvvfe4fv062dnZZzqGeOYnJ4xAIMDY2Bj3799ndHQUp9NJQ0MDv/jFL+js7Dy3EOVx5GtxcZGkpCTKysowmUwA0dwpv9+PSqWKpnT09vYyNTXFysoKJSUlZy5erVYbXbBMS0tDqVQyPT3Np59+yvb2NleuXKG2tvZUwtWvGj8pYfj9fsbGxrh58yaDg4MYDAbeeecd3nzzTbKzs881br+1tcXdu3fZ29ujpaWFurq6p34uCALhcDiaNFhZWUl+fj57e3v09/ej0+nIyck5l7FqNBo6OzspKSnhiy++4Msvv+TWrVvY7XYCgQBtbW0/u6jVT0YYwWCQr7/+mk8//ZSlpSXy8/Pp6uri4sWLFBUVnft4VlZWePjwIYFAgIsXL1JdXR392ZPJBoIgIBKJKC4u5sKFC9y9e5f79+9TXFx8bsIAUCqVFBUV8dZbb5GcnMxXX33F9PQ0R0dHHBwccPXqVbRa7bmNJ9b8JIThcDgYGhri5s2bzM/PU1VVxXvvvcelS5dQqVTnOhZBEHA6nczOzrK9vU1paSk1NTWkpaU98/ePZw2TyURnZydTU1PRVyye1AUFBeTk5GAymfj4448ZHx/H5/MB0NHR8bNJSnzlheH1erl9+zY3b97EZrPR2NjIjRs3aGpqOndRwGNzbnh4mKmpKVJSUn40wnO8m0+tVlNdXU1xcTGTk5NYLBbm5+cpKSk5d3FIpVJaWlpQKpVIpVKGh4f54x//iMvl4t1330Wn053reGLBKy0Mu93OnTt3+Nvf/sba2hpNTU28//77tLS0xGyhyu12c//+faanp6murqazs/MHTZBjs0okEqHX66mrq2NiYoLl5WV6enowmUzfO9ucJVqtlvb29ujY+vv7+cc//gHA1atXycrKOvcxnSev7HYvn8/HgwcP+NOf/sTq6iqXL1/mN7/5zbmtT3wfm5ubTExMcHh4SFVVFXV1dScaj9ls5sKFC7jdbnp6etjY2DjD0f4wIpGIxsZGfv3rX9PZ2cn29jYffvghX3/9NR6PJ2bjOg9eSWF4vV5u3brFn//8Z/b29mhtbeWXv/wljY2NKJXKmI1ra2uL0dFRHA5HdNvqSc2OvLw8Lly4gEKhwGKxYLVaOTo6OqMR/zhKpZL6+nref/99Wltbsdvt/OMf/+CTTz5hf38/ZuM6a145Ybjdbvr6+vjb3/7G6uoqly5d4je/+Q2NjY0xz/OZnJzk4cOHqNVqLl++TEFBwYmPoVarKSkpoaysDHi8cr6wsBD1RWKBRCKhoaGBf/mXf6Gzs5OtrS3++te/0tPTg8vlitm4zpJXzsfo7e3lr3/9KxsbGzQ1NfGLX/yCmpoapNLYfpRgMMjExATDw8NR3yIjI+OFjmUwGGhpaWFra4upqSkGBwcpKSmJ+UJbbW0tAIeHh4yOjnLz5k0kEgnXrl2L+UPptHllZgyv18vw8DCff/45s7OzVFdX88EHH8Qs+vQkgUCApaUlrFYrPp+P4uJiqqqqXtisk8vltLa2Ul9fH82h2tnZOeVRn5zjNJL333+f2tpapqen+cc//sHw8PBPzud4ZYSxsLDA3//+d+bm5qiqquLGjRsx9ymO2d3dpbe3l52dnWh6x8uENCUSCQUFBVRVVaFQKFhZWcFiseB2u09x1C8+tvb2dn71q19RVFSExWLh008/xWKxxHpop8orIQybzUZvby+9vb0kJSVx48YNWlpaYm5aHLO+vs7t27dxuVx0dHRQU1Pz0seUyWQUFxdTXV1NMBikr6+P5eXlUxjty5OUlER7ezvvv/8+RqORO3fucOfOHXZ3d2M9tFMj7oXhcDjo7u6OiqKzs5OLFy+SnJwc66EBj32Lubk5ZmZm0Gg0XLhwgfz8/FM5dnp6Oq+99hppaWkMDg4yOjpKvNSu0Ov1vPnmm1y/fh2ZTEZfXx/37t3DbrfHeminQlwLIxKJMDs7y6effhqNQL3++utxk7MTDAaZn5/HYrEgCAJFRUWUlZWdmiOq1+tpb28nNzeXlZUVJicn48LXOEar1XLt2jXefPNN9vf3+ctf/sLo6Gish3UqxLUwLBYLX331FWtra5SWlnL9+nWKi4tjPawoR0dHPHjwgOnpaUpKSmhra8NgMJza8WUyGTk5OdH1kOXlZUZHR2O6rvFtSktL+eUvf0lVVRWrq6vcu3cPi8US0/DyaRC3wvB4PNy+fZvu7m6Kior41a9+FVeigMcpKX19fWxublJbW3tmq+5ms5nm5mYODw/p7u5mfX391M/xMhxn5dbU1DA2NsbHH3/8yvsbcSmMo6MjJicnGRoawuv10traSnt7e9w42/C4cqHVamVpaQmFQkFdXR15eXlncq7S0lKuXLmCIAj09vYyPz9/Jud5UeRyOW1tbVy5coWjoyMePnyIxWLB6/XGemgvTFwKY3l5mdu3b+N2u2ltbaWuri7uMjrn5+cZHBwEoKamhuLi4jNb5EpNTaW2thaTyYTdbsdiscSVrwGQkpJCfX09FRUVuN1uHj58GHcCPglxJ4xQKMT4+Dh3795FqVTy1ltvRdMj4onR0VH6+vpISUnh0qVLZ1o8QCQSkZmZSW1tLampqczMzDAyMhLdJxEv5Ofnc/36dUwmE3fv3uXhw4f4/f5YD+uFiCthhEIh5ubmGB8fx+v1UlFRQUtLywvVij0rIpEIOzs7TExMsLGxQUlJCS0tLWdevECpVNLe3k5jYyNLS0vcu3cv7pL41Go1HR0d1NbWYrfbefToEfPz8wQCgVgP7cTElTB2d3e5c+cOKysr1NXV0dbWFleiAHA6nYyPj7O6uopOp6OiooLc3Nwzz9WSSqXU1NRQV1eHy+VifHyctbW1Mz3ni2Aymairq6OkpASbzUZ3d3dMU+dflLgSxvr6Ot3d3bhcLrq6ur5TQCAe2Nzc5M6dOxweHtLQ0EBVVdW5JdDpdLpoyc3Dw0PGxsaw2Wzncu6TUFVVxbVr14hEInz11VdYrdZYD+nExI0wjo6OWFpawm63YzAY4rbpydzcHI8ePUKhUHD58uVTW+V+XjIzM7l48SIGg4GBgQFGRkbiZjX8mKysLNrb2zEajczPzzM3N0cwGIz1sE5EXAgjHA5jsViYmZnBYDBQV1cXd/3kwuEw29vbTE9Ps7W1RVZWFs3NzefebyIlJYWuri5yc3MZHR3l0aNHcRcWlUgkFBcXU1ZWhkKhYGlpidnZ2bgLFvwQcXHneb1e+vv7sVgsmM1mLl68GBdZs0/i9XoZGhpidnaWlJQUamtrycnJOfc+dyqVCrPZTGlpKX6/n/n5eRYWFqLdX+MFtVpNc3Mz9fX1rK2tce/ePQ4ODmI9rOcmLoThcDiYmZlhZ2cnupch3gp8HRwc0NPTw9raGjU1NTQ0NMRsc45araa8vJzS0lL29/fp6+tja2srJmP5PkQiEQ0NDTQ3N7O3t0dvb+8rtRoec2F4PB6Wl5dxOp0YDAby8vLQarVnVtT4RQiFQiwvLzMyMkIwGKStrS3mayvl5eVcvXqVcDjMnTt3WFhYiOl4nkVmZibV1dUolUrW19fZ2Nh4ZUK3MRfG2toa4+PjKJVKGhsb47LKts1mY3x8PFrkoLq6mpSUlJiO6bgDlFarZWZmBqvVGpcObmZmJkVFRVFfY2trK+6CBc8i5sJYXFzk0aNHKJVKWlpaSE9Pj/WQnkIQBCYmJhgcHCQpKYmmpiays7NjHhiQyWSUlpZSXFyMWCzGarUyOzsbd09kvV5PVVUVJpMp2uswHA7Helg/SkyvbiQSYXV1laWlpajdHI8LegMDA1itVsrKyujo6DjzVe7nJSkpiZaWFqqrq1lcXIxLB1epVEb7Gi4tLTEzMxN34n0WMRPGcWrF1tYWoVCI1NTUF66qcVYEg0GWl5eZmZnB4/FgNpupqamJm4jZcSnNpqam6CpzvCUXKhQKzGYz2dnZrK+vMzs7G3fh5WcRM2F4PB7m5+c5PDwkMzOT7OzsuCvBsr29TX9/P/v7+xQUFFBZWYler4+rwEBOTk60h8Xa2hpWq/WpognHwY319fWY+CBisRiDwUBmZiZisTjagzzewsvfJmbCODg4iD49SktLz7Xk/fNitVrp6elBJpPR0dFx7qvcz0t+fn50JhsZGXmqYsfCwgI3b97k7t27Md35l5aWFt2vsry8HPeF2mImjMPDQ+bn5/H7/ZSUlMRdWyuPx8PExATj4+OkpaXR1dUVd4GBY0wmE1evXiUnJ4eBgQGGhoYIBoN4vV4mJiZ48OABs7OzMX1KGwwGSkpKUCqVrK6uxl1m8LeJmTDcbjdra2sEAgFycnJiHv58kuMiB1arlUgkQnFxMZWVlXHjdH8bjUZDU1NTNKPVYrFEa1FNT08TCoXQ6/Xn2lHq2+j1evLz81EoFGxsbMR9NZGYCcPlcrGxsUEoFCIrK+tMWwqfFIfDQV9fH+vr65SUlFBTUxNX43sWmZmZVFRUYDAY2N3dpb+/ny+++ILFxcVoQYVYZhPodDry8/ORyWSsr6+zt7cXs7E8DzERRigU4vDwkEAggEqlwmAwxHxd4ElWVlbo7u7m6OiIzs7Op9qExStisZiKigouXLiAIAjcunWLjz76KNqeuKamJqbBDY1GQ35+PnK5nPX19cSM8W0EQcDhcOBwONBqtZhMprgJf8LjZMFjM0qpVNLU1ERubm6sh/Vc5OXlcfnyZVQqFQ8ePGB0dJRIJEJZWRlZWVkxffjIZDKysrJQKBTY7XYcDkfMxvI8nPs3FQ6HsdvtOJ1OUlJSyMjIOPcM1e+reRSJRJibm2NiYgKxWExpaWk0neFVQK/X09DQgMlkwuFw4PV6SUlJIT09PS5C4UlJSWg0GiKRCG63O67XM2IijP39fY6OjtDpdBiNxnMVhiAI2O12FhYW2N3dfSo94bj0y/T0NKWlpXR0dMSoOkmYSChIMBgiGBY4SWZRRkYGaWlpaDQaNBoNBoMhLkRxjFarJTk5Gb/fj91uj9u8qXNvKhEKhTg4OMDj8aDRaEhOTj73GWN8fJwHDx6gUqm4dOkSbW1tSKVSHA4H/f39rK2t8Zvf/IYLFy7EwMzzELEvs7y6w9qhAvS55BZmUmiQ8DzLimKxGKlUSigUIhAI4PF44qoqoFarRa/X4/f72d3dxWQyxeWMfO7CCIfDOJ1OPB4PycnJ6HS6c7d9j46OmJubY2trC7vdTigUori4mImJCba3t0lKSqKysvLMfIunV86/+bsQhNARTtsqa8vLrG8fsHsYwscG2/Yi9ipLKUrTkKL8/u9KEATcbjdut5tQKITf78dms7G9vU1hYWHMm+vAYydcr9fj8/mw2+14vd6EMOCxMA4ODvB6veTk5KDX6891xhCJRNTW1uL1evnss88YGRlhe3ubzMxM/H4/KpWKyspKioqKznQMx+IQib+5BN4tfKuD9I3uM+7IJLe4kkrTKnvjvfR+OUL39DU6O+t5q9HI95W09ng8WK1WHA4HaWlpiMVi/H4/MzMz5OTkkJeXF/Pon1arRafTRWeMeN3uGtMZ4/jpcd4Xq7CwEJPJhFqt5osvvmB6epq+vj5UKhXNzc10dXWdafpHJBJBEASkUhly2ePP7tmeY+HhbQatOtbymikrqqQ6TYnDN8CjR+OMT4gQKZMoKm/FrIFn9ZB6MpGwrq4uep6BgQFSUlLIysqKub+RlJSETqeLLvLFqzBi4ny7XC58Ph8qlQqtVnvuPgY8ntK7urr43e9+R3NzM4FAgNXVVQKBwJn6PQcHB9hsNnw+H6FQmGDED0TYX19itHeRdXsEbUEOxjQlCl02ac0tlOdrSN8eYctiZcwmsP89LsPOzg4zMzMIgkBnZyf/+q//SmlpKVarlcHBQZxO55l8ppOg0WjQarUEg0EODg7iNgX93IURiUTwer34fD7kcnlM1zB0Ol3UlzCZTEgkEkZHR/nkk08YGBg41b5ygiCwuLjIhx9+yO3bt9nf32d1bYOR4X6OjuY5OtxmecnJnkuKOlmLWg2IkpEYy8jONJAjseE/2GZ1L4L7e1Ke5HJ5tJRnV1cXXV1dVFVV4fV6sVgsLCwsxPwJrVQqUavV0fsgXrNsz92UEgQBn89HIBBAJBLFNH8HHj9lNzc3SU1NJTU1lZ2dHR48eEAwGMTn89HY2Iher39pE8TtdjM6OsqHH35IT08PoVCImZkZvvryS9JNHcjlIJNG8Hi8OA68+ANKkIkBORKpErlaiUolRSEF8fdEOLOysrh27RpJSUmUl5c/tcvPbrfT399PWlramfpPP4ZMJkOpVCIWiwmFQolw7TGCIOD3+wkGg4hEopiYUU+yuLjI8PAwKpWK9957L9o2a3R0lLW1Nd544w26urooKSl54X0YgiCws7PD8vIy+/v70X0Ra6srTE7Nsu9ooyA5hSyTQMS2w+ryLnsHBtAABAgKSoLSLFJSjOSbRCR9z1UzGo3U1tYil8ujD5y8vDwuXLjAF198QU9PT3TRMlZ8WxjxFEp+kpiYUn6/H7/fH425x4JIJILNZmNychKbzUZqairXrl3jD3/4A7///e+pqalhZ2eH/v5+FhYWXmqfsiAIhMNhwuEwYrE4KrBIJEQwKCIQMqLLNFNz0UxpyhFH418zdG+I4ckRZmYsrBxpoKSdsqoKakxi9N/zLFEoFOj1+qfaOxuNRjo7O8nJycFqtTIxMYHH44nZk1omk6FSqRCJRHEtjHO/K4+FEQgEEIvFMQsfer1eBgYGsFgsZGVlRftPADQ0NKDRaLhz5w42m41AIEA4HH5hEYvFYtLS0sjKykKpVEZvyoyMdAryC0nSpCJJT6Hs2g26Dm7jH3rIXPcm/7uRQob8iJDIROZrzdQ3llEih5NE/ZVKJRUVFZSVlTE8PMz8/DwzMzOYzeaY9EeXy+UoFIqEML6NIAgEAoFoNCJW20QPDw+5d+8ec3NzdHR00NHREV1oUqvV1NfXo9frmZ+fx2QyvbSA9Xo99fX13LhxA4/Hw8LCApWVlbx2tYv0NBPIk9GUXqbtNRky/TzLIQ2CzkCKTIIuMx9DSSWl6apnhml/DJVKRU1NDcPDw2xsbNDd3U1GRkZMNodJpVLkcnlUGAkf4wkEQYjpFxKJRFhZWWFmZga/309tbS1ms/k7N39+fn50r/LLmnxisZjy8nL+8Ic/cHh4yIcffkhBQQHt7RfQ6Y4ro6ST2fAGr1deIRARERFJkIhESGQypHI5spfQZllZGRcvXuTmzZv09vbS2toaE2E8aUrG+j74Ic7djjmORMUyGrW2thbtfpqfn09ZWdkz+/uJxWKUSmX0CfeySKVScnJyKCoqQq1Wo1arSU5ORiz+57FFMhVKbTI6vZ5kXRJarQa1Uo5czHPlSn0fmZmZtLW1odPpoi2YDw8PX/oznZRQKBQNPkil0rgqLPEk5y6M45tNoVAQiURiYmOOjIzQ09ODwWDgypUr516IQSKRRKMy57XApVAoKCwspLKyEqVSycTEBBaL5dzXEQKBAD6fD0EQkMlkMU9R+T5iMmPI5XLkcjmCIJz7hfF4PIyNjfLfwkcAAB9TSURBVDE5OUl2djYXL16MWR+O8zYltFotzc3N0dXwvr6+p0rtnAdPCkMqlSaEET2hWIxCoYiJMHw+H1arlfn5ecLhMOXl5dGFsPPkOIfpvJFIJDQ2NtLU1MTu7i4DAwPn3gYsGAzi9/uJRCIJYTyJSCSKCiMSiZyrMLa2tnj48CEHBwdUV1dTWVkZV73DzxqxWEx2djZVVVXo9Xo2NzeZnp4+17KexxkFgiBETcp4JCbCOHZoj/cMnBfLy8vcuXOHQCDApUuXqKioOLdzxwsSiYSCggLq6uoQi8X09/czNzd3buf3+/3RBUa5XJ4QxjESiYSkpCSUSiU+n4+jo6Mzd8CP87NmZ2eZn5/HaDTS1tYWly0HzoOUlBRee+01cnJyGBkZYWho6Nxmbq/Xi8vlQiwWo9VqY54G/33ExMc4Tltwu90cHh6euTD8fj9TU1PMzs6iUCgoKyujuLg4Lna0xYKkpCRaW1spLCzEZrMxNTV1br6G2+3G6XSiUChISUmJy917EANhSKVS9Ho9arWao6MjDg4Ozrxfgsvliq5yV1ZW0traGqMiB/GBRCIhNTWVyspKTCYT6+vrDA8Pn4uv4XK5cDqdqFQqTCZTTNJSnoeYmFLfnjHOWhg2m42BgQH29/dpbGyktrY2bm3b86S8vJyOjg78fj/d3d0sLy+f+TldLheHh4coFArS0tLiqqbYk8RUGEdHR2duSjkcDiwWC2tra2i1Wurq6n62vsW3KSgo4MqVK8hkMgYGBpidnT1zs9btduNwOKLCSPgY3yCVSjEajWg0Gg4PD9nf3z+zGUMQBCwWC4ODgyiVSurr6ykoKPjZ+hbfJjk5merqarKzs3E6nczOzrKxsXFmayyCIOB0OnG5XCiVSoxGY9xei5jMGCaTCa1Wy97eHjab7cyEEQqFGB4eZmhoiKysLC5dukRaWtqZnOtVJTU1lbq6OnJzc5mbm2NwcPDMVsOPjo5wOp0Eg8Ho3u94JSZRKYPBQHJyMoeHh2xvb5/JPuRwOMzm5ibj4+PY7XbMZjMNDQ1xa9PGCqlUSmtrK62trayvr3Pv3j22t7dP/TzhcJjt7W08Hk+06Fq8zhYQo2rnCoUiWuHc6XSeSYHf/f19RkZG2NzcJCUlhcrKymgKeYJ/clwlvb6+nmAwyOTkJMvLy6duTrndblZXVwkGg2RnZ8csP+15idldotfrSU1NRRCE6JPkNFlZWeHu3bv4fD5aWlooLy+P+f7yeEWlUlFaWkpBQQFer5exsTFWVlZO9Rwul4uVlRWCwSB5eXlx1SjoWcRMGElJSRQUFKBSqVhdXT3VfgmRSASLxcLIyAg6nY7Ozs5EJOpHSEtL4/Lly2RlZTE0NMTg4OCproYfHh6ytLSE3+9PzBg/hFarpaCgALlczvLyMjab7VSOGwqFWF9fZ2Zmhr29PfLz82lsbPxZL+g9D3q9ns7OTgoLC5mZmeHRo0enWqDtuOeix+OJ1vGKZ2JqSpWXl6NUKpmdnWVtbe1Ujut2u+nr62N+fp7s7Gzq6urIyMhI+BY/glwup7S0lPLyckQiEYuLi1it1lNJ8hQEgd3d3eg1zsvLQ6/X/8i7YktMZwyz2YxWq2VpaenUhLG7u8uDBw/Y3d2lsbGRmpqauN0+GW9IpVLKysqoqanB4/HQ19d3Ktfl8PCQjY0NvF4vBoOB7OzsuI5IQQyFcdx6KiMjI/pEsdvtL7WmEQgEWFhYYHx8HLFYTHt7e0yLi72KlJSU8NprryGRSLh79y6zs7MvdbxAIMDKygobGxsYDAYKCgrifraAGAoDHosjPz+foqIijo6OmJmZeeEm7YIgsLq6yvj4OF6vl/z8fMxm8ytxEeKJ9PR0WltbSUlJYWFhgdnZ2Re+JvDPfuk2my3aFjreZwuIsTDgcUn+6upqvF4v4+PjL5zhGQqFGB0dZXR0lLS0NJqbm0lPT0+YUSfkeCPTceWU+fl5pqamXjic7vP5GB8fZ2Njg+LiYsxm8ysRNo+5MHJycqirqyMUCjE+Pv7C0an9/X36+/tZXl6mpqaGtra2uM31j3eO+4Q0NDSwvr7O119//ULh9Egkws7ODktLS/h8PgoLC8nJyUkI43kwGAyUl5cjlUpZWlpidXX1xH6Gz+djYWEBq9VKKBSiuro6JkUOfkrU1dXR2tqKw+Ggp6eHzc3NEx9jd3c3uqc8NTWV3NzcuN1/8W1iLgypVEpGRkZ0TWNubi5axeN52dzcpL+/H7fbHQ05ajSahBn1EphMJmprazEYDNhsNiwWy4nNXIvFwsOHD6P90rOyss5otKdPzIUBjwsPNzc3U1lZyfz8PD09Pbhcrud+/9TUFP39/Wi12ujqbYKXJzs7m4aGBpKTkxkbG2N8fDxaRfDHCAQCDA8PMz4+Hq3fZTQaz3jEp0dcCEMqlVJXV0dtbS3r6+v09vayt7f3XO91Op2Mj48zMzNDVlYWV65cifs8nFcFo9HIlStXKCoqYnR0lN7e3uda8AsGgywvLzM1NcXh4SGlpaXU1NS8MmYUxIkwRCIRJpOJkpISkpKSovWOfixM6PP5mJ6eZn5+Pto9qKSkJOF0nxIKhYLa2loqKytxOBxMTk6yubn5o7v8dnZ26O7uxmazUVhYiNlsxmAwvFKmbVwI45jc3Fyam5uRy+Xcv3+fsbGxH/z93d1denp62N3dxWw2U1VVlXC4T5nU1FTKy8vJyMjAbrczOjrK7u7uD75nbm6OL7/8Ep/PR0dHB+Xl5ec02tMjroRhNBp5/fXXKSoqYnh4mAcPHvxgItvCwgLd3d0Eg0G6urp+lgXUzoOSkhIuXryIWCzm7t2731ugTRAEHA4HIyMjWK1WMjIy6OrqeiUzm+NKGCqViqqqKsxmM+FwmKmpKcbHx5+51fLw8BCr1cry8jI6nY7GxsZX8gK8CmRmZnLp0iX0ej2jo6PRlsnfxu1209/fz8TEBHq9nsbGRsrLy18p3+KYuBKGSCRCrVZHCw9vb2/zySeffGfTzHHH06mpKdRqNRUVFeTn57+QGXXc4cntduN2uwkEAtF/Ozo6iuuWuyfB6/VycHCA1+s98Xs1Gg01NTUUFhbicrmwWCzRnuhPsrOzw2effcbCwgItLS1cuXLllU33jythHFNaWsrbb7+NXq+np6eHR48ePXURDg8P6e7uZm5ujpqaGjo6Ol64OHMwGGRvb4+ZmRnGx8fZ29sjEAiws7OD1WplcXHxXIsevwzhcBifz4fH48Hn8z21FrS8vExfX98L145KTU2lpqaGoqIi1tbWePDgwVPfSyAQYGxsjNHRUeRyOVeuXKGmpualP1OsiEthaDQa6uvrqaqqIhAI0NPTw8DAQFQc29vbDA4OsrOzQ319PY2NjS9cnygQCLC+vk53dze3b99mdXUVv9/PysoKfX19DA0NndomqrNmf3+fgYEBPv/8cwYGBp5K4xgZGeF///d/GR0dfeHj19bW0tLSwt7eHnfv3n2qaEJfXx9ffvkl4XCYxsZGqqur47Zm1PNwvsIQIghChO8E+wSBb5usqampvNbVSUtLCwsLC9y6dYuVlRUODg6iaQY5OTk0NTW9VLKgTCbD7XZjtVqZmprC5XIhlUpxOp3RfSKnXcXkuHWZVCo91dCy3+9nZmaGvr4+LBbLU2bT+vo6/f39L1WjtrKykqtXr6LX61lcXGRpaQmXy8X6+jqfffYZk5OT1NTU8NZbb73yZYrON/83EiIc8OMPQUgQIRELIESIhCEikiFVKlEpxBynmDU2NnHodLO8vMz4xAS9vb2o1Wr6+vqis8rLOtzhcJhQKPTU61n/dpocN4457ap/x92Kjk2pJ1epj3vfvcxnEYlElJSUkJeXx9jYGNPT08hkMtbW1picnESr1dLZ2UlTU9Mr33fknBPjw4Scm9iXZrEs7bDiUiDRp5KdqUenloDbidflJaBIRZNXTmVpCm0dbSwvL9H9oIdbt27hcrnY29tDrVZjt9v5/PPPX8jBE4lECIKAx+Nhbm6OlZUVPB4P9+/fZ2tri5mZGebm5lCr1UgkEtbW1qLveVGOZ7UHDx5gs9mYmJjgj3/8Y7Qf4csed3Nzk9HRUba3t6PtFXJychAEgcnJSXw+H5OTk/z5z38GOPFnEYvFeL1etre3cTqd9Pb2MjY2ht1uR6PR8MYbb3DhwoVX1uF+EpFwnj2vBD++tRGW7v8PNz8d4OacEUV5K29dr6AiLUJgycKqZYF5dwrSitd57a2LXK3W49le5+//+1f+9Kc/MTE5iUajITs7m4yMjBc2RY5vpkAggMPhYHNzk1AoRG5uLgaDAbvdzt7eHnK5nNTUVFJSUhCLxc99Az/ZsveY433n6+vrrK+vYzQao+0IHjvKIh6/7bum5Y+dSyQS4XQ6o6LQaDSYTCYMBgPhcBiLxcL6+jq5ubmUl5cjFotPnMUsFoujaxV2uz1alDstzcTvf/97/u3f/o2CgvwTHTNeOd8ZQyRFqtZj1AqoQ4fYdtWoCzUk5xRQmCEmopKQrHbjvj/PyNf/4CtBjD7jbTqycrl8sZ3x0WGsc3OIxWLKysqoq6sjEAjg9XpP/PSTSCSIRCLcbjdbW1scHR1FS7tkZmaiUCiiXX/y8vLIzs5GLpf/SJdV0eP/RKInWg9/04BSgG/ueoqLi4lEItGe12KxBEEQHv9YxOPf/aZx5fN8quOWXTs7OwiCwMHBAcnJyRQUFJCfn4/P58Nut7O7u0taWhoVFRXI5fITh24lEgkSiQS5XM709DRfffUVAX+AxsZGrl574ycjCjh3U0qCVJ9Oem4exYUFZG5koy2soKq+kYYUCeKqaggZSXL+v6z09jDTk8PDzusUmaSUlZbywQcf4AuGWVxcxGQy0dDQEE1XP15/eO6RfCOM/f19xsbGiEQiuN1url27Rl1dHcPDwzx69IikpCTa29tpaGh4DmE8Pr8giBCJpUikYiQiASJhwpEI4W8mm+MnPEBEEBCJJYglYiQICOEQ4dDjAIXwlMC+n+N+2XNzczx48IC1tTVyc3Npb2+nvr4er9eLx+PBZrPR1NTEv//7v6NQKE60K++4d+Lx3pft7W2ys7MpLC7h9//n9zRVFxB27bDv9HMUEBCJIoik0sefjTCRsJiwWElSkhqjTok4ztOmzn/zrVgCMhkyuQypTIZMLkehkHwTHlOAVIdOI0EecuJzuTlwBvH4pWj0yVzouIjb6+fzzz9naWmJR48eUVJSQlFR0Ymd2eObc29vD7vdHt0bnpWVRXFxMTabDYPBgE6nIzc3l7KysucwpcIIoSD+QJhQRIJEJkMulyKViBARIfItYTyeSAQQixAJYcLBIEF/kHAYkMuRymRIxT8eOjw+XjAYZHZ2FrfbjclkoqCgIOpjpKamolAoSE1NpaSk5MSm1OOZTczKygrDw8PMTM9grqriVx98wMWORjTBTWZ7H9FrdWEL69CnaNGrpUhDbkIeBza3EreimLo6M9eas0mSxbcyzl8YkTBEIkTCAQT/Pk7bMgszs6SlyxEd7eJzDPJoIYA7p4GiOjPVGWKSBQARBmMKly9fJhgM8pe//IUHDx6g1+t55513KCwsfKEtkwqFApVKRVJSEpFIBI1Gg1QqJRKJEAgECIVCiESi6LF/+BwSENz4D1dZtS6xtOXFm1xMVlU9FTkK0r71bR/7ExzOsm6dY3TZx4E0jeziEgoKMshUSzjJWr5MJosGCEQiUTQTQCQSEYlE8Pl8URPuxz/Ld1lbW+OTTz6lu7sbhUrNG2+8zZtX6knyLzF4r5e7g6tsS1LRZhuRyuXIZRKkQgQhssvepodJRxiZxkRHfSZJsvje3nr+whCJADEigogC+xzYlpif0KLeVxBansI21U+/Nch2xiXaWuppKZKT8YR/nZ6eTldXF06nky+++IJbt24RCoX47W9/+0KhW7FYjE6no6CgAI/HQ3JycrTVrlqtRqlUnuwGCnsIH86w1Ps3/vLJLNOaTsy/1vL/vGXmjdxn/H5gD//UZzz40z/4//rgsOg13vw/Jt7MzOSktfqOBXHsuzxpWspkMtRq9QtnHx8cHPDJJ5/w97//HYVCyTu/fJ+r166gj6yy0P1X/vzJNuM0cOW9y7zdkU+6TIpUDKKIm4g3E71+Hu+QHFUkQEiIAAlhPAOBx16qBIlUhlwhQ66SIYTd+Oxb7NjC7Ih8uIOP7ewniwiKRCKysrK4fv06wWCQjz76iE8++YRQKMSNGzcwm80nGolMJiM7O5tLly4RCoXIyclBoVBQVFSEWCxGoVCQkZHx/AcUK5HpFSRpjvDbrEyuS9kxtFBVauJCbipPBzLDBL1rzE0+ouf2ICMzJlSpYYTkJFQKEdJvvqbnRSKRoNFo0Ov1aDSapwRdUlLClStXKC4ufv4DfsPxAuvHH39MKBji+vW3eOuN6+TnaNnpGaTnswcMr5bC5TbK6uqpy3pyxTsF0FDvM+AXDlCkqZBIIEKcpl18w/kLQxBAEIggRZAlo0vPp7CiCnOugpDMix4Xu95hPKuPmO3L5X5JNvoGI8Wap7/G4uJibty4QTAY5LPPPuPWrVuEw+ForarnTUeQy+VkZGSQnp4O/HN9o7y8nKKiIkQi0clSG2R6VFkFFLU0UNO8x8SOG9dMH4uWYqztqdQoIDoBhvfw7s9h2fGw7DOhScqnrKSA8jITmVoxihOa4RqNhsLCQrRaLWlpaSQlJUV/1tDQQHp6+om2/YbDYVZXV/n444/56KOPiEQi3LjxLjfeeZeC/HSITGAdGaZn1IUvp4jGthoKTc/6rlJJzpTRItlHUCpRSsXPFW2LJTGbMQTEIFGjTDKQkpFJRooCkbwdoykNIRwk+Jdu7k/c53Z3FeXpdRSXJn3nKAUFBbz77rtIpVJu377NrVu3cDqd/PrXv6a+vv65R/NklOj4/xUKxQuukYhALEFhysFobqZ0fIg91zi71kYGF9vIKJaQI3/8HbC7gmdljn2ZBl9mCRpfEgaZFKVCivQFfFO9Xh/NL1MoFE91LMrJySE9Pf1EptT8/Dz//d//zd27d1Gr1Vy7do0b77xLcVEh4IHdeWwrNhb2FIQrTWTl6kj+7mUCQJmkJ0OhICISgVh8kokwJsQgKiUFqQSpRIpIIkem1KDR6dBIgORs1MkZNNX1Mf/F3/liap7ZhW22D56dxiAWiyktLUWhUKBWq/nb3/5Gd3c38Hjba3V19VNPzfMhBPgJivWI0usor9glbBvHsj5D7+A6NSk55JgkQADn6hZbcw4UhmSyq+S47V4IBAgFQ4Re4NIolcrv7Rh1EqF7PB6mpqb47LPP+Prrr1GpVNy4cYMbN26Qn//NWoXghL1tjg59uIQkJGo1SRqQfp/rIAKxXBnX5tOTxCAqFYJgiGAwRCgUJBQMEPAHCWtl37hjDo6OPBwFJMjUenQGPWrlD5syOTk53LhxA5VKxaeffsrt27ex2+387ne/48KFC+e8UUYAwoQiSiISPYUlZSRnrLG6vop1YIS5ai0dJiNi9lm2+ZnfScJQEsScH2RT5SMUFjjjxqk/iMfjYWhoiP/+7/9maGiInJwc3nvvPa5cuUJu7hPRg4gACBwH1uLeNjoh5yuMsA+ffYXtuXmmZudYX3GgSM6k966MSKYauc+J73COmZ5ZRoMVZDVfoelSCWXpP/ykE4vFZGZm8uabbyKXy/noo4+YmZnh//7f/8va2hpXrlz555PuXBCIhCASVpFaVE6peov8j5ZZmOzDMm9mtVxOlt+K7UhgTVZOs36bEu0uvZIwoUjs7rHFxUW6u7u5d+8eVquV/Px83n33Xd58883vZsuK5JBsQK2TocGO+8iD0y16vIj5qkwLP8D5CkMIEnTvs3MQwSXSkGaUIBJ22ZqdYupAg8xpw7W1xIJNQbjsbS5evcqbl3IoNTxfaC81NZU33ngDk8nEX//6VwYGBnA4HPh8Prq6usjPzz+3CiJCOASRCJKMIoz5XupHN5hbnWZhdonuPB8dAQtesQlRcTnJKRAOTyCNhDn9Np0/js/nY2VlhS+//JJbt26xs7NDY2MjH3zwAS0tLRgMhu++SawGYyHpeRkUG9cY3VtneW6H3TwTBd8pHyVAJEQgGHkciZRJkcS5k3G+whDLkRsKyGh+n9dNHVS6pAgqPSkpWnRqGWJfIX6XmfKgBnFKEYWleZSkSDiJIaTX62ltbUUul5Oenk5fXx83b95kfn6eN95446V2+50IIYwgRAirclBnKmg09zA9O8nduVFuhXeRaGzISgvINWeQplzlMCR8Y56cLy6Xi3v37vHVV18xPj6OQqHg7bff5vXXX6exsfEHfDQlKCsoNtfQVjvN7Ow0k939TJZcpdqY9K1r5uLIvsvyWhCSkskqMqGTieN6JeOchaFAkVpMbmoxuY1ndxqVSkV7ezsFBQUYjUa++uorxsbG8Pl87OzsUFtbS3Z29rOfhC+NGJAgkYiRSCREBB3yJA2FTVXUW2d5MPyQ/vlC1DXZXKnPorlQTWpQypxIjCCIEUskSKSSM79p7HY7a2trjI2Nce/ePebn5zEYDFy/fp13332XgoKCHzmCBEgjo6yDC29sYgkuM7xyj9F7YVIixeSp5KjkMqQSkAiHOPc8bB8o0UqTojlj8Uz8Nyp4CTIzM3nnnXfIy8ujp6eHoaEhxsbGMJvNvP3221y8ePEMqhYKQIRIJEQ4HCLgD4M0CWV5HWVVj8h/8AjrRghLTTttukIKZCALBQiFw4QiESKRCBFB+O4ux1PEZrNx//59Pv/8c6anp1EoFLS1tXH58mUaGxufdrJ/BHFGPUWvSfhAcoe0hxZmBm7y51kTaaZU0lJ06NQalMokklMzSc/PJCsjGa1MFPduyE9aGPA4YpWVlYXJZEKtVvPo0SNmZ2dxuVxMTk5SW1tLeXk5xcXFp9CnLwJ+B66dRRbGppiaTCHJrcXcWEF1gZmM0lYa0ufYEqlIqirBkJmEyj3PwfwsVquVpXUPgcVFZi0blNXkoNPKUJ3SHRQOh5mfn2dycpKxsTGsVis7OzuYTCaam5u5fv06zc3NJ2/qItOhzGqj+aoCnS6FlMltlt0KlMl69DotSUoNCpWRFFMWefnpZJww/ytW/OSFAY+jVrW1teTm5nLp0iVu375Nb28vMzMzDA0NcfnyZS5dukRxcTFqtfolHHQBwe/kaHOfneVdDhwBvEYba458igpMqLMv0NhhR+wzoujIojQdgvv7HKwesn8UQqoTEYwccbC6y15+Br4k2Yn8q2cRCATweDxYrVa6u7v5+uuvWVtbIysri2vXrtHZ2UlFRQV6vf4lOh1JkaTXUnq1mKy2IL4QiCQSJFIxYpEEkVjyOItaKXllbrjz3cEXB4TDYcbHx+nv72dkZIT19XXC4TDJycmUlJRE+0K8WHg3guDdxbk5h3XBxpxdgcSYR3lVAaW5euRHhxwuLOBAjriolNQkBZqDZRwrs4zPLDO/HSGozyO/ykxpcTa5yXI0LzFjbGxs0NfXx/DwMHNzc7jdbsRicbSIxIULF6iurn6lasqeFz87YRzj9/ujT9Genh6sVitSqZTS0lKam5sxm81kZGSg1+vR6XRotdq4voEEQcDlcuF0OnE6nezs7DA9Pc3g4CAzMzOEw2Gqq6vp7OyMNu18lcvbnDU/W2HA49ljfX2dtbU15ubmHtv5S0vs7u4iCAJZWVnU1tZSX19PZWXliZzS82Z1dZWpqSkmJycZHx9nc3OTcDgcbcpTXl5OWVkZBQUFZGVlxbXI44GftTCeJBwOMz09TW9vL48ePWJlZQVBEEhLS8NkMmEymUhPTyclJQWDwYDRaMRgMJCcnIxGozm3cbrdbhwOR/S1v7+P3W5ne3ubnZ0d7HY7drsdQRDIzc3lwoULdHR0UFlZ+Ur0vosXEsJ4gmAwyOH/3979tigKhVEAP5BoiVZYQi8sKoK+/8epIEoLikL7J1qWuy9m78PMdHeXWWZnWTg/uHRfCwe9ee/xeMTxeMR2u8ViscBsNsNkMsF6vUae52g0GhgMBhgMBuj1elKU0Gq1ZAOf2q37etfu+927yuvLr+bfVBHCjwG8dM/u93usVissl0sZ8/kcSZLAtm10u1351Fq/30en00Gz2USj0eDnET6IwfiFOI4xnU4xmUwQhiG22y3yPJdWDnVSDoC0CrquK2sS13Vh2zZM05RhWRZM05Qz17fb7WlkWSbVNKfTCefzGVmWoSgKOduufh+PhxymGg6HGI1GGI/HaLfb//jq/d8YjN8oy1LaCA+HAzabDcIwRBiGiKIIURRhvV5LwbEKhAqHbduo1WqyJbxarcKyLFQqFSlhzvMc1+tV5mmaPgUDAOr1OoIgQBAEcrfq9XpyZzBNE4ZhfML7GGIwPuh+v8uzfRzHSJIEh8MB5/NZPhuQZRnSNEWe51KmADwfiAKeH5+AlyOq1WoVtm1LsBzHgeM4sq7xPE/Gn79/oJ9hMD5RURTSYLjb7RDHMS6Xi/TGqk7coihQliUqlQoMw4BhGDJXpQWe58H3ffi+j1arxb9WvxiD8Rfcbjdcr1ep33m/LlDdVOoOotYqam4Yxpv1CH09BoNIg6s0Ig0Gg0iDwSDSYDCINBgMIg0Gg0iDwSDSYDCINBgMIg0Gg0iDwSDSYDCINBgMIg0Gg0iDwSDSYDCINBgMIg0Gg0iDwSDSYDCINBgMIo3vBL6lFb5XHwsAAAAASUVORK5CYII=)
maths-General
maths-
In the given fig. if C is the centre of Circle PQC = 25° and PRC =15° then QCR = i
![](data:image/png;base64,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)
In the given fig. if C is the centre of Circle PQC = 25° and PRC =15° then QCR = i
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALIAAAC6CAYAAAAK2RcFAAAgAElEQVR4nO2951NbaZr//VFAGQRCEggQQeQcDNiAc+q23XanCdtbW/tqf7+/Y/6Ip+qpfV5t1c7W7vTsTE+Pc+i22zgRjMk5iZwklFCWzvPCg6bdYbptA8K0PlXqwm18zq1zvuc+133dVxAJgiCQIME7jjjeA0iQYCdICDnBgSAh5AQHgoSQExwIEkJOcCBICDnBgSAh5AQHgoSQExwIEkJOcCBICDnBgSAh5AQHgoSQExwIEkLeNQSIRohGo0TiPZRfANJ4D+DAIggIET9B7xZuf5hgOApIEInEiJNkyGRyZAoZMqmEJIkIUbzH+46TEPKuIYKIH//KMDMDL+ged7AQ0pFm0pOtjSJyO3GGU5Bm1VBRU0xNvhpNvIf8DpMQ8m4hEiESiWFrBe/oPR5dt/LQU0rl0XpOl4kQLw0xNOZhVTXNuO0i0YsN1OmlaCTxHvi7SULIu4lUhSpNR75RRbJcTsBnQJtbRdPxTFLc6WgCV7nz+A7PBCUyg5n0VhPlungP+t0ksdjbTSRyZGlGsnOyycoxYzAVkFdURX39ERqPf8y5FguVSdOsj7ygo3+VZUc03iN+Z0kIeS8QABGIRCD62x9BjUyuQq0UIxGHCAYDRMPhuA7zXSYh5N1GiBKJRolGBQREiCRiBILgHmVuco4pmwxSMsnJ1ZGcnLgdb0rCRt4jREIEIezF59lkYzNCwNrLxMIWNmUlltpGWuuyydQlbsebkrhyu41IDCIREpGfiGeJ5dFunqenoXR6cGe0cujXhRQeaqSpWIVRHu/BvrskhLxHiAAhGiLk9+D1p5OkLMHSkkt2kQVLpgpt4k68FYnLt+sIiIAIcqTqTDKLaqk9Uk6WWI5MlUyyVo4i3kM8ACSEvNuIJSRJJYilCiRKPbosC5bsbNLjPa4DRmKZvJsIEaJ+Ly6PB4/bhc/jxOV0splwF+84CSHvGgKC345jfoL+oQlGR0dZmh5mdHiCgckNlgNCIipuB0mYFruGCBERokISPnUB2SUyWsJZ5KfKiAYihESJiLedRJQoYriLCAFCjjU21tdYtfvZEjQodQaMmXrStTKU8R7fASIh5F0gGAwSiUSIRkEQSxBLpEhEUURCCFE0iiBAVBCBWIxUKkUqTbwY35bEFXxNBEEgGo3GPtt/DofDeDwenE4nXq+XUChEOBwhIghEowIBv49wyI9SLkehVCGRSBCJJchkMtRqNSkpKahUKpKSkhCJRIhEIsRiMRKJBLE4sZT5KRJCfg28Xi8LCwssLy+zsrLC+vo6m5ubeDwefD4fkUgEsVgcE+K38Xg8BAIBlEolarUakUj0t1n75QMhEomQSCSoVCq0Wi1paWkYDAaysrIwm82YTCYkkkSw8o+REPKPEAqF8Hg8bG1t4fF4cDgcrK6usri4yNLSEqurq9hsNhwOBx6Ph1AohFKpJDU1leTkZJKSkkhKSiIYDLK2tobVaiUcDlNcXExeXh7hcBi/34/f78fpdOJ2uwkGg8hkMrRaLampqRgMBkwmE2azmaysLAwGAykpKajVajQaTeyBSJAQ8g/i9/uZmJigv7+f4eFhJiYm2NzcRCqVkpqailarRafTkZ+fj0ajQaFQIJfLUSqVKJVKZDIZEokEiUTCwsICV69epaOjA4VCQUVFBR9++CGCIPzN/Pi7oLc/Pp+Pra0tXC4X8/Pz9PX14fF4kEgkmEwmSktLqa2tpaKigpycnHhfrn1BQsh/Y21tjfn5eebn51laWmJlZYWVlRXW1tZwOByIxWL0ej0Wi4X8/Hzy8/PJycnBaDSSlpb2o3ZsX18ft2/fRiKRkJWVRVFREQ0NDaSkpPzg7weDQex2O6urqywsLGC1WpmYmGBubg6Hw8Hi4iI+n4/l5WVevHiByWQiOzubrKwscnJySE5O3s3LtG/5xQs5FAqxuLhId3c3jx8/pqenB5fLRXp6OkVFRbS2tlJQUEBWVhZarRa1Wo1KpYrNvklJSf/w+HNzc9hsNnJycqiqqsLpdNLZ2cmRI0fQaL6fbiqTycjMzCQtLY28vDwaGhpiNrjNZmNxcZGZmRlGR0fp6OggGAySm5tLfX09R48epbq6mvT0X94G+C/W/Wa32xkYGGBgYICJiQk2NjYIhUIA6HQ68vLyKCsro7i4mMLCQpTK1/P6BoNBRkZGuHnzJr29vZjNZvLz8xkaGkKlUvFv//ZvlJWVvdG4JycnGRoaYmJigsXFRbxeLyKRiOTkZDIyMigqKqK6upqamhrk8l9GbOgvbkbe2tpieXmZvr4+njx5Qn9/Py6XC7PZTGtrK0eOHMFiscQWbFKp9I3cXy6XiydPnjA9PU1NTQ0nT55EJBLx/Plz5ubmWFpaoqSk5LWPrdPpOHToEDU1NQSDQVZXVxkcHKSzs5O+vj4GBgbo6+tjfn4el8tFRUUFaWlpKBQHO8buFyVkm81Ge3s7Dx48YHp6GplMRnV1NXl5eeTn51NSUkJRUdFPmgs/B4fDQXd3N8vLy1y8eJHa2lrcbjd6vZ6VlRVmZ2dZXV0lIyPjtcW8vZBUKBSkpKSQlpZGdnY2tbW1TE9PY7VaGRwcZGBggPLyck6fPk1LS8uBFvMvQsh2u52ZmRm6u7t5/vw5MzMzJCcnc+jQId577z2qqqqQyWQ7dj6fzxezjVUqFbm5uajVaiQSCXV1dbhcLkZHR8nOzubUqVNvfW69Xo9er6e5uRmn00l3dzcPHz6ks7OTp0+fYrfbWVpaora2loKCAtRq9Q590/3DgRey3W7n0aNHXL16lbGxMTIzMzl//jyNjY3k5+djMpl2VMSCIDA1NcXg4CApKSkUFRVhMBgAUCgUNDQ0sLi4yLNnz0hNTaW5uXlHz6/VamlqaiI3N5e6ujqePHlCd3c3AwMDHD58mMuXL3PkyJEdPed+4MAKORQKMTAwwKNHj+ju7mZ1dRWLxUJrayunTp2iuLh4187d399PV1cXmZmZHD9+nLS0tNjf5efnU1RUxN27d5mYmGBtbY3U1NQd3dhISUkhJSWF/Px8jEYjGo2Gzs5Oenp62NzcZGZmhtbW1l29BnvNgRSy1+ult7eX69ev8+TJE2QyGadPn+bChQu7/mr1eDyMjo5itVppaGigpqbmlfMpFIrYTp3f72dsbAyDwYBOt/MlhpKSkmhqaqK0tJTGxkZu3rxJd3c3CwsLbGxscOnSJQoKCg6EZ0Pyu9/97nfxHsROsrq6yrVr1/j8888ZGxvDZDLx3nvvce7cOaqrq5HL5bu2revz+ZiamuKbb75ha2uLkydP0tjY+L3zCYKAw+HAbrfj8/liMRW7wXb8hslkQqfTIZFI2NjYoK+vD6vVSlJSEpmZme+8mA/MjCwIAnNzc3z11VdcvXo1tri5cuUKJ0+e/MHNh51mdXU1tklRX19PQUHBD/5eWloara2tLC4u0tfXR15eHocOHdrVuInk5GROnDhBQUEBX331FV988QUdHR34fD4CgQCtra0YjcZdO/9uc2CEPD8/zx/+8IfYdvDFixc5c+YMlZWVeyJiAKvVyrNnzwA4fPgw+fn5P/h7SqWS8vJyMjMzaW9vZ3p6ms3NzV0xL75Lbm4u77//PhkZGdy+fZuurq5YBN+ZM2cwmUy7Pobd4J0XciQSYWhoiJs3b3L37l3EYjGnT5/mo48+eqOdszclEAgwMzPD9PQ0tbW11NbW/qgwRSIRarWavLw8jEYjGxsbDA8PU19fvyeuMZPJ9Iqp0dXVxRdffIHb7ea9996joKDgnYuqe6dt5HA4zPj4OH/605+4ceMGycnJ/PrXv+bSpUtYLJY9C0iPRCLMzs7y9OlTlpaWqKur48yZMz+5sRIMBvF6vayvr+P3+8nOzt7TOAmDwUBBQQGBQIChoSGmpqZi///bnpZ3gXdayENDQ/zXf/0XDx8+xGAwcPnyZS5evEheXt6eZlW4XC7a29sZGBhAr9dz9OjRn/U2UCqVSKVSuru7mZqaoqys7Eft6t1AKpXGRLvt/56eniYajZKenv5OBR+9k6ZFNBplbGyM69ev8+jRI3Q6HZ999hlnzpzZEzvzu6yvr9PR0YHNZuP999+nvLz8Z/07rVZLcXExWq2W2dlZ5ubmCAQCyGSyPX2119TUoNPpkMlk3Llzhzt37iAWi1EoFOTk5LwTZsY7mQy2uLjIn//8Z27fvk1WVha/+c1vOHHiRFxEDLC0tMT4+DjhcJjy8vLXWjDpdDqKi4sxGAzMzc0xPDxMIBDYxdH+MDk5OXz44Ye89957eDwebt68yf3791lZWdnzsbwJ75xpMTs7y7Vr17h37x4qlYpPP/2UDz74IC6vQUEQWFlZ4dmzZ4yOjpKfn8+FCxde64Hazu/zeDxMTk4SDocpKytDpVLt4sh/GJ1Oh9FoxO12MzExwfz8PHK5nNzc3H0fcPROzchOp5O7d+9y7do1NBoNv/nNbzh58iRarTYu4wmFQvT29jI0NITZbKa5uflHMz9+DKlUSmVlJeXl5aytrdHb24vdbt+lEf80+fn5/Pa3v+XYsWMsLCxw8+ZNOjo6cDgccRvTz+GdEfLm5iZ37tzh/v37SCQSTpw4wblz53ZtR+znEAgE6O7uZnh4GIvFQktLyxvNpNtxESqVio2NDaxWKx6PZxdG/NNIJBLKysq4fPkyhw8fZnZ2ls8//5z+/v64jOfn8k4s9oLBIC9evODLL7/E4XBw6dIlzp8/H9edqGg0ysrKClarFZ/PR15eHhaL5Y0XRpmZmdTW1jI2NkZ/fz+ZmZlUVVXt8Kh/PnV1dcDLuOre3l5ycnJiWS77cfG372fkaDRKX18fX3/9NQsLC1gslthWazxZX19naGgIv99Pfn4+ZrP5rW5weno6R44cQa/X09PTw9DQ0A6O9vWRyWTU1tZy+vRpsrOzefbsGVevXmV9fT2u4/ox9rWQBUFgaWmJO3fu0NXVRWFhIe+99x5FRUVxLzM1NTXFo0ePkMvlHDt2DLPZ/FbHU6lU1NTUkJOTw/z8PCMjIzidzh0a7Zshl8s5fvw4Fy5cIBAIcPfuXbq7u3G73XEd1w+xr4Vst9vp6uri2bNnRCIRTp48ydGjR/fFCnpycpLe3l7UajXNzc1kZGS81fHEYjEZGRnk5eUhl8tZWVlhZmYmLq64b2M2mzl+/Dg1NTW4XC6+/vpr+vr6iET2V1HcfS3kwcFBbt26hc/no6Wlhba2trhvnUYiEdbX15mbm8Pr9caylnci40IikWCxWKioqMDr9fL8+XPW1tZ2YNRvjlQqpaioiCtXrlBYWEhHRwcPHjxgc3MzruP6LvtSyIIg4PF46OjoYGBggJKSEi5fvrwvquq43W56enpYXV2loKCAkpKSHQ30MZvNtLS0IJFI6OjoYHp6eseO/abI5XLa2to4duwYAL29vfT19eHz+eI8sr+zL4Xscrno6elhdHQUuVwey7TYD3lmGxsbPHr0iPX1derr66msrNzR46enp9PY2IhSqWRkZITp6WnC+6AjqlKppLm5mZaWFtxuNzdv3mRkZCTew4qxL4U8Pz/P7du3cTgcHD16lIaGhn1hFwuCwOLiIgMDA4TDYerr68nLy9vRc8hkMrKzs8nJyUEsFjM3N8f8/Py+sEnz8vK4cuUKZrOZnp4eurq68Hq97IcaP/tSyFNTU3R2diKVSjlz5gylpaXxHhLwclNmdnYWt9uNTqfDYrHsSvywQqGgsrKS0tJSVlZW6O7ujrsHA0Cj0VBXV0d1dTVSqZTR0VEGBwfZ2tqK99D2l5DD4TBWq5WxsbFYCdbvJm/Gc2wjIyOMjY2Rnp5OVVUVer1+V84lCAI1NTU0NTWxsrLCw4cPsdlsu3Ku10Wj0XDkyBHq6+uZn5/n66+/3hdj21dCdrvdPH78mOnpaSorK2lubt431SU9Hg/d3d1MT0/HspJ3y9wRiUSYzWbKy8sJh8NMTEywtLS0K+d6E0pLS2lpaSEQCNDV1cX8/Hy8h7S/hOxwOHj8+DFzc3M0NDTQ2Ni4I+WrdgK73U5/fz+rq6uUlJRQXl6+q5syUqmU7OxszGYzgiAwMTHBwsIC0Wj8m/SlpqZSWVmJTqdjbW2NyclJbDZbXG3lfSPkYDAYK+4nl8spKysjOzs73sMCXqb5T05OYrfbYwE+aWlpux5zkJqaSmtrK7m5ufT19fHixYt9seiDl+lQNTU16PV6hoeHGR4ejlUzjQf7QsiCIDAzM8PIyAhqtZqqqqp9I2J4uYvX19eHQqGgrq5uzyLukpOTY9nYw8PDvHjxAr/fvyfn/inUajWNjY1YLBYmJibo6emJq195XwhZJBIxODjIixcvyMzM5OjRo3Hfwfs2/f39dHR0oNfrOXny5K4t8r6LVCqNVcf3+/3Mzs6yvLy8L/zKUqmUiooKSktLWV1dZWBgIK6elX0h5GAwyPj4OBMTE+j1eqqqqvasFsVPsZ0tMTc3h9FopLa2dk8XoElJSbEQUb/fT19fHxsbG3t2/h9DJBKRnp6O2WxGKpWytrbG0tJS3OzkuAs5Go2ytrYW641hMBjeqGbwbuD1ehkfH2dtbY2UlBTy8vLQ6XR7Prbc3Fyam5sRi8U8efKE2dnZPT3/j/HtQKftLOx4xYbEXS1ut5uxsTG2trYwmUxkZmbGPURzm9XVVR4/fszW1haNjY2UlJTEZRx6vZ7Dhw+TkpISa7mwH7wX8HJLva6uDq1Wy/DwcKw2xl4TdyFv21eRSITy8vK4pi59l4WFBR4/fozP5+Pw4cNxE7JKpYqV2HK5XMzMzLC2trYvxKzT6WLm1ujoaNzeFnEX8srKCsPDw4hEIioqKt46rncnEAQBn8/H7OwsCwsLqNXqmN80XiQnJ1NSUkJ2djZLS0v09/fHLa/v26jVakpKStBqtczPz7O4uBiXByzuQrbZbLGnOC8vb194K0KhEFNTU8zOzpKcnExhYeG+eMDKyspoaGjA4XDQ0dER91hleGknm0wm0tLS8Pl8bGxsxOUBi6uQBUFgY2OD1dVVkpKSyMnJ2RdRbj6fj87OTiYmJiguLubQoUP7wouSn59Pc3NzLHt7YWEh3kMCXnpW9Ho9Wq0Wr9fL8vLynm+OxE3IgiDgcrli/e2Sk5NJT0/fFxm6drudnp4e1tbWqKqqoqqqal80NNdqtRQWFpKamordbmd2dnZfmBcARqORgoKCWEHHvR5X3IQcCoVYWlpic3OT5ORkDAbDvpiNg8Eg8/PzzM3NIRaLKS0tJTMzM97DAl76bvV6PeXl5eh0OiYnJxkZGSEYDMZ7aBiNRvLz84lEIkxPT+/55kjc/Fx+vx+r1Yrb7cZkMpGRkbEvZuPFxUUGBwcBKCoqIicn5+0ClyIetpxePEExIoWGlBQFireYPuRyOa2trWxubjI6Ooper6e4uDju2TN6vZ7c3FxWVlZYWFjA5XLt6fnjNiMHg0HW1tbw+/2kp6ej0+niLmRBEBgcHKSvrw+DwUBTU9Nbeioc+NYmmRroovPxM551jzKy6MIJvOn+l0wmo6amhuLiYlZWVujv798XiaBpaWmx4o1ra2t7Hmwftxk5EAhgs9kIBoNkZWXteIuuN2G7G9To6CgnT57k8OHDb7jI8xHybDA/OcvqqhNXOELEZcU22cPgeAXGqsOcqMqgWPf6s6hIJCIlJYWCggJSUlKw2WxMTU2h1+vjGrut0WgwGAxEo1HsdvueBzfFdUa22+0EAgFSU1PRarVxFbIgCDHbOBgMkpubi8VieYNXtgBBK/bJJ3xzv59HE1JE2VXUVKSSFxlitOMpN9tnmNp4u3oV2dnZseD+7ULh8UQmk5GamkokEmFzc3PPI+HiNiNvC9nv96PVauMu5O1KmB6Ph8LCQgoKCt5sqzwaImgdYLH/KUMreYSLCjiRYcasqETutHFIocauSyFd8XZeEJPJxNGjR2Nlbbc7ncaTlJQURCIRW1tbvxwhh0IhHA4HwWAwJuR4MjU1xePHjxGLxRw/fvxHOzL9JEII78w4i6PjbIgrSc3MQ6eSkaQtI7sti1+VQ0CkRp8uRwDe9NFNTk6mpqaG9vZ2Xrx4weTkJG63G41GE7cJQaFQxDxPfr+faDS6ZwFWcTMtwuEwbrebcDhMcnJy3HPzpqam6O3tRS6Xc/jw4beI+Yji93hw2DdxbvkIRqOIxABqUJvIzjJiMciRy0QEefNFH/zdd5ucnMzy8jKjo6N4vd63OOLbIRaL0Wg0qFQqgsHgnpb7ipuQo9Eofr8fQRBQq9Vxcx+Fw2FWV1exWq0EAgEyMzMpKCh4c5+2SIxMrSRJFMY1O8rs8CjWmEs1gHdpnrnZRTbcvrcWslgspqysjNra2li+Y7xjlZVKJUqlkkgksqf+7bgKeXsbU6lUxu116PF46OrqYmlpicLCQiorK9+u/IA4iRRTNpmZaSg2xpjvus/T/kkmtlw4ViYYHhqjb3SZDXfgrUyLbQoKCmhqaiIUCtHV1RXXbWuRSIREIkEikRCNRvc0kyVuNvK2kJOSkuLaB9nhcPDgwQMWFhZiVY3ebjtaijSngYLmJdrG77M1/Cdu/3/DjN/PIVenRZmSj7kolxKlDBlvL2SDwUBdXR23bt1icnKS6elpGhoaUCqVb3nkNyNeQo7rjLy9GIiXkKPRKEtLS4yMjBAIBKiqqsJisbzlUcWQVoGp8QIXL7ZxoUKCcvE5nfee8HhoE482m5yKYjJ1anbiW2+XDbBYLCgUCqamppiZmYlLXp9IJCIpKQmpVBqbqPYq9SmuM7JEIkEmk8WldoUgCLGaDD6fD7PZTEFBwc48VCI5MkMFZSeTUGZVUzrvZMWnQJWRT0FFEcWZUpLFbz8bb6PRaKitrWVhYYHZ2VmeP39OTk7OazfmeVtEIhFSqRSpVEokEiEcDiMIwp6YjXHNKRKJRIjF4rjYx9FolOHhYXp7ezEYDDQ2NmIwGHbwDCoU2bWUZtey25XrxGIxtbW1LC0t8de//pWOjg7a2tr2XMjw93ZrgiDEPntB3EwLkUhEJBIhEonEJaPA7/fT29vLyMgIubm5NDU1xeXG7wQikYicnBxKS0uJRCJMTU0xNze35xnNgiDE7qdYLEYikezZJBU3IW87ysPh8J4HYW+bFSMjI9jtdoqKiigrK9t1F+BuPrAymSzWdWn7bRMPD8b25LTXQo6babH9RaPR6J73yXA6nQwNDbG5uYnBYMBisZCamror5wqHwzidTlZXV/F6vaSkpJCRkYFGo9nxYH2dTkdbWxsPHjygt7cXs9lMdnb2nu2uCYJAOBwmHA4jFouRSqUHX8jbPkdBEPY8UspqtdLV1QVAfX09ubm5u3KeQCBAb28v9+7diwX1bFfoOX36NBUVFTta+kCr1dLW1sbExAT379/HbDZz9uzZPXPFbQt5e0bey7IOcZ2Rk5KSCIVC+Hy+PduXFwSB0dFRnj9/jtFo5NixY7vSeDIUCjE2NsZf//pX/vCHPzA7O4tCoYj1mvb7/chkMoqLi3dsZpbJZFgsFvLy8giFQlitVubn5ykoKNgzz1AoFCIUCiEWi/d0tzauNrJCoUAkEuH1evfMvHA4HExOTrK4uBjbTNiNRZ7b7ebRo0fcu3cPq9VKJBJha2uLQCDA5OQkt27d4smTJzseJSaVSrFYLBQXF+PxeOjp6dnTJo+BQIBAIIBEItnT/YG4CTkpKYnk5GSkUilut3tPmhD6fD5GR0dZWFggNTUVi8WC0WjclcTS7ZrGo6Oj39uc8Pl8jIyMMDU1tSsbF8XFxRw9epRIJMKDBw+wWq07fo4fYvth9fl8yGSyPTUt4ipknU6HXC7H6XTuSY7X6uoqT548YXNzk0OHDu14R6Zv43a72dzc/MEHdHv7VhCEXTGnsrKyaGpqQqFQMDQ0tGctzvx+fywQTKlU7mmNvLgJWSaTxYS8ubmJ0+ncdb/n8vIyjx8/xu12c/jw4V1rsuNwOOjq6mJsbOyV7/TtGxuJRGK7YDuNTCajqKgIk8mE3+9nZmaGxcXFXd223i7vEI1GUavVe54RH7fF3reF7HA4cDgcu7adKQgCgUCAmZkZlpeXY/05dnYn76V9uD3r379/H4DCwsLY4kcQBILBIOFwGK1Wy+rqKh0dHVRXV+94zWWtVktVVRUzMzPMzs7S1dXF6dOnd23TZzvjRyKRkJ6evudBS3EVcnp6OjKZDIfDsasz8rYHYXx8nOTk5F2rVTE0NMS1a9dob29HIpFw5swZzGYzS0tLsXjn7XWB3W5ncnKSf//3f+f8+fNcunRpR8tySSQSampqmJmZobOzk2fPnlFfX79rQvZ4PGxsbMTqJv9ihKxQKMjMzESpVDI3N7erLa6CwSBPnz5laGiI4uJiWlpadrQE1vLyMi9evOCrr76ir68PQRBobW3lypUrlJSUsLCwwNTUFH6/P/YWWlhYoL29ncHBQa5evYrT6eTo0aOUl5fv2NgKCgqor6/n0aNHDA4OsrCwgNls3hXb1W63s7KyEquZvNct5eIqZLPZjFarZWNjg7W1NSKRyK54EBwOBy9evGBhYYG2tjbq6up2zDW0uLjIvXv3+Mtf/sL8/DwVFRWcP3+eo0ePYjKZkMvllJSUkJOTgyAISKVSxGIxVVVVlJaW8uDBA27dusUf//hH5ubmuHLlCk1NTTsi5pSUFIqLi8nMzGRubo7x8XGKi4t3xW++vr6O1WpFIpGQn5+/5zmYcROyVColKyuL9PR03G436+vrMbfNTrK1tcX09HSsW1RRURGZmZlvbYt7vV6eP3/O3bt36enpwev1cuTIEc6ePcuxY8dIT0+P/a5EIvleTuJ2Y53k5GQUCgXffPMN/f39MZPjxIkTb12PWSQSYTQaqa6uxul0MjAwQFFREXq9fsdn5bW1Naanp2MdYfe6qmpcwziTk5PR6/UoFAo8Hg82my2WUr5TzM/P093djUgkoqqqipXfnfYAABoySURBVLy8vLe6iZFIBKfTSUdHB7dv3+bp06doNBouXrzIpUuXsFgsrzXbFxYWkpmZSUlJCX/5y194/vw5NpsNt9vNe++9R35+/lu9plUqFUeOHGF5eZmxsTG6u7upr6/f8eqi6+vrLC4uYjKZyMvL2/PqpXHvcaDX68nKyoplaxiNxh29CKOjo3R2dsZaz26XdXpTpqamuHnzJl9//TVOp5OKigpOnTpFS0sLxcXFb3RMtVrN4cOHUalUZGdn8/z5c65evcr4+DiXLl3i9OnTbyxmuVxOdXU1g4ODMZt8fX19R6/xdtUol8uFWq3ekTfe67IvhFxSUoLT6WRycpLc3Nwdu8jbO2jT09McP378rWKO7XY7w8PD3L9/nydPnuDxeGhoaODy5cscP378rU0itVrNkSNHyM3NxWQyce3aNQYHBwkEArhcLpqamsjPz3/t84jFYtLS0qiqqiInJwen08nw8PCOldgKh8OsrKzgdDpjZbNUKtVbH/d1kfzud7/73Z6f9VuEQiHcbjcLCwv4fD7y8vJ2pI9IMBhkYmKCu3fvsrKywsmTJzlz5swbCc5ut9Pe3s7vf/97njx5gl6v54MPPuDjjz+mqqpqR29ccnIyJpMJs9mMSCRiYGCAvr4+fD4fOp0Oo9H4RrOd1+tlaWmJtbU1QqEQGRkZb/12gpchsb29vQwODqJUKjl8+DDl5eVvfdzXZV/MyNXV1XR0dDAwMEBLS8uOHHdzc5POzk42NzcpLy+nvLz8tUUcCoUYGBjg/v37dHR0sLy8TFlZGWfPnuXMmTO71p3VaDRy5syZmD/26dOntLe3s7a2xokTJ17LRPJ4PFitVp48ecLY2FhsQVlfX099ff1bj3Vzc5MXL17gcrkoLy+noKDgrY/5JsRdyBqNBovFglqtxmazsbq6uiMhnXNzc3R0dBAKhTh27NhrX+CtrS36+vq4ceMGDx48QCQSceLECa5cuUJZWdmepEVttzIuKSnh2rVrdHZ2srq6isfj4fTp0xiNxn8YnulyuRgeHubp06d0dHQwPT3N5uYmIpGIhYWFHSmxtW1yeb3eWLOeeBB3IYtEIlJTU8nJyWF0dBSbzcbCwgImk+mNY2iDwSDT09OMjIyQmppKfn4+ycnJP/sBWVpa4s6dO9y7dy+2Em9tbeXkyZPU1tbuWTCMVCrFYDBw6tQpNBoNDx48YHh4mP/+7/9mfHycixcvcuTIkR8V4vDwMLdv32ZiYgKdTsfHH3/M1NQUk5OTzM7OMjw8TGVl5VutSVZXV5mdncVgMFBYWBi3zldxt5HhpZhdLhdutxuPx4NUKsVsNr9R4Ml28uX169dpb29HEAT0ej02m43l5WUkEgkqleoHg3U8Hg/Dw8PcunWLGzduMD8/T0lJCZ9++imffvop+fn5ccn4VqlUFBUVYTabYx1GJyYmYu0NVCoVarX6lbEFg0G+/PJLbt26RXJyMp988gmXL1+msLCQra0trFYroVDojdO8BEHAZrPx5MkT+vr6sFgsfPDBB3ErRrlvhJyUlITL5aK/v5+trS2qqqre6AK73W7u3r3L9evXWVhYIBKJsLGxQU9PD2NjYwQCAbRaLXq9/pUbv7W1RWdnJ7///e+5c+cOUqmU8+fP89FHH9HY2Lgv2qZtV4U3mUyxouTDw8Oxh/Xb12tjY4MvvviC4eFhjh8/zq9+9SuMRiOpqam43W6ePXvG+vo6NTU1mM3m1x5LMBiku7ubZ8+eEYlEaG5upqmpKW7FduJuWmyTlZVFWVkZt2/fZnx8nPn5ebKzs1/bvHA4HDx9+pSlpSVaW1uxWCxEo9FYYNLjx49jW+FlZWUATExM0N7ezuPHjxkbG4stti5evEhRUdFufN03Ynv7Nysri7S0NBQKBX19fdy+fZvV1VVOnTpFbW0tarWa+fl5PB4P2dnZ1NTUxF75KSkpVFZWkpKSwuLiItPT01RXV39vRv8pvF4vT548YXR0lPr6elpaWuLazGjfCFkmk5Gbm0t+fj6Tk5MMDQ3F0tt/LoIgxCLNdDod//Iv/8KpU6eIRqO4XC6ePn3KN998Q29vL2lpaUilUgKBAHfu3OHGjRt4PB4aGxv58MMPqa2tjWun03+ETCajpaWFvLw87t69y71797h9+3asJ4vBYGBgYACVSkVjY+P3kmuzsrIoLy/H4XAwMjJCeXk51dXVrzVprK6uMjIygtPpfKN/v9PsGyHD35uHO51Ourq6MBqN5Obm/uzF1fLyMiMjI4TDYYqKimhoaIiFa2ZlZSGXywmFQkxPTzM9Pc3s7Cxra2uxxNDW1lbOnj3L4cOH494l6adQKBRYLBbef/99UlJSaG9vZ35+nv/4j/+Iza7JycmUlZV9L+5aq9XS2NjI4uIiw8PD5OXlUVZW9rOFuLGxwcjISGzGLywsjGshStgnNvI2EokEjUbD2toa3d3dANTU1Pzs1952QLsgCLS0tHyvY2lycjIikYiNjQ36+/tjvmGTycTly5f5zW9+s2+aQ/5cUlNTKSsrIysrC5/PFysDZrPZUKvVFBUVUVpa+soWt0gkQi6Xs76+HotDOXTo0M9eqHV2dnL37l0ikQhtbW00NTXFveNA3HtRfxuJRBIr/SSXy5mZmaG/v/9nNR8MBoP09fXR399PRkYGR44c+d4CbTtje3R0lN7eXgBOnTrFv/7rv3L+/Pm4+UDflqSkJKqrq/n444/5p3/6JyoqKmKty+bn57+XqS0Wi8nJyaGsrAypVIrVamVqaupnZXS73W66urro6urCYDBw4sSJfdGne1/NyPDyIovFYhwOB/Pz89jtdkwm0z8UWTgcZnFxkS+//JLp6WlOnjzJuXPnXpmNrVYr9+/f5+7du4yPj6PX6zl//jyffvopra2t72zdt222fc5FRUWo1WpCoRAulwuv14vP50OpVJKamhpzO0okEoLBIJOTk2xubqJSqTCZTK+En36Xra0tnj17xu3bt9na2uLs2bOcOnUq7mYF7EMhA7E+FKOjo/T19aHX66mpqfnRRM2NjQ06Ozvp6OhApVLx3nvvUVtbG/t7q9XKjRs3+NOf/sTo6CjFxcV89tlnXLx4kby8vD1NW99t5HI5OTk5lJSUIJFImJ6eZnBwEKfTiU6nIyMj45U1h9/vZ3FxkbW1NYxGY8yT80MMDw/zxz/+kcXFRQ4fPszp06fJycnZi6/1k+xLIUulUnQ6HXNzcwwNDREKhTAajRgMhh9ckIyPj3P16lVWV1dpbm7m7NmzpKWl4fP5ePDgAZ9//jkPHjwgHA5TX1/PpUuXOHXqFHq9/p2yh38ucrk8Nrtu++dnZmaYmJhga2sLnU5HSkoKGo2GlJQUhoaGeP78OXq9nsbGxh+8xhsbG3z11Vdcv34dvV7PZ599RmVl5b5ZFO9LIcNLF1M4HMbj8TAzM4Pb7cZsNmMwGF5Z+EWjUR4/fsz169dJT0/n448/prCwELfbzZMnT/jf//1fnj17hkaj4dKlS/z2t7+lqakpbq0J9pLtEFmDwYDNZovZzNvdl9RqNUajMdbRSqlUUlpaSnp6+iuztsfj4dGjR9y9e5etrS2OHz/OhQsX9pU5tm+FDC+d9zKZjBcvXjA1NYXRaMRsNsfCJgVBYH19nXv37vH8+XOampr44IMPcLlcfP755/zxj39kYWGBuro6Ll++zOnTpykuLt7TwiHxRCQSoVAoMBgMGAwGFAoFi4uL9Pf3x6otmc1m/H4/c3NzeDweNBoNWVlZr6wvxsfH+c///E+GhoZobW3lww8/fPM+hLvEvhby9gLFbrdjtVpZX19HpVJRWFiIRCIhEAjQ3d1NZ2dnzHcsFov55ptvuHPnTqwQy2effcbZs2d3vHbEu4JcLsdsNlNYWBhrVTw7O4vT6cTj8aBQKJDL5VitVlZXVykqKorZvrOzs1y7do1vvvkGo9HIP//zP9Pc3LzvJoN9LWR4GRCj1+vxeDw8f/4cp9NJaWkpBoOBjY0Nbty4weTkJBkZGQQCAZ49e0Zvby/p6el88sknfPLJJ5SVle2LlXW80Wg05OTkkJeXh9/vZ3h4mMHBQWQyGQaDIZZNU1FRQWVlJeFwmC+++IJr166h0Wj44IMPOHbsWNybe/4Q+17IIpEIvV6PTCZjbm4Oq9Uaa/vr8Xi4fv06vb29CIKAx+MhEolQXl7Ohx9+yEcffURGRsaB8kq8LWq1moKCglhgvsvlwuFwsLa2xsTEBOFwmIKCAmQyGYODg/zlL39hcXGRs2fP8tFHH5GdnR3XnuE/xjtzh8vLy/n000/58ssvefjwIdFoFL1ez8zMDOPj46ysrFBeXs6xY8c4e/YsFRUVBAIBwuEw0Wh0Txuz7Fe2mw/B37NQUlJSuHv3Lg8fPsTlcpGbm8vIyAhzc3Osr69jt9tpbm7mxIkT5OXl7UsRwzsk5NTUVI4cOYLL5eKLL77g4cOHsddjNBqNNdfZXp3PzMzEhPxLF/B32e5tKAgCi4uLOJ1OvF4vXq83JuBwOIxSqeTYsWN88sknVFVV7VsRA4iEd+wuLywscPfuXf7whz/w8OFDfD5frPWu0WiMNZzZrjz5jn29PePbreEkEgk+n4/Z2dlYlo5KpebEyRP83//zf/ngg0v73jzbn6OLhgmGBETSJJK+s1+RlZXF6dOnsVqtTE9Ps7GxgcVioa2tjZycHHw+H8FgcM87Rb2LbPf50Gg0BAIBRkdHCQQC+Hw+Kisr+NWnn3Ls+LF9L2LYN0IO4FuZYWF2iVWfQEAiRyKEIeAjjAxRWgEZeXkUGyXIxWLy8vK4ePEi0WiU9vb2WOekhoYGioqKEIlEBAKBxGz8E2y3v/D5fAwMDODxeJDL5Zw8eZKLF97n/fPnSNfpvtf8fSeawe808Rdy1EPIPs5YxzM6e+ZZiKqR6nWkJYUQbMvYHEGcmgrMDa2EjhRSkyFHAtTV1aHRaEhKSuLBgwex+OXtkrFSqRRBEOLSjHK/s21WCIJAKBRicHCQgYEBBgcH0Wj+lt936X0MqRr8znU23T6CEUAkRiIWI06SkZQkRy6TIZNJSUqSIImzsuMuZNf0KBPtf+HesIvZpAryi7Ipz01GIw0jeDLZXJqgv+cpY7cX8AQ+xNVaR0u2CJlMRkVFBaFQCKlUyqNHj7hz5w6RSIQPPviAkpKSV1bpCb6PSCSir6+PP//5z/T09JCRkcH771/g3PnzGDOzwbOAbaidnhfDdM8LbKlM5OWmYlT68Ns2WdtKQZFdRe3hWqoKNcQznybuQl6YsHLnWg+dsgrMv3qfo215tMbCW8ME1rvJcv4/fHH/a765lY5HZsScZqJALUYE1NbWolKpUCqV3Lhxg2vXruHz+fjwww8pLCz8RcRUvAnbhVWuXr0ae5tduXKFDz/8CK32ZQxFJBQgahthpecm1x/DmrGJ98+XcijdhWN6hN4+O7bkSaZ8UoKyOlqyZajF8Zma4yzkKLOb8GghDX+1mYraLCyZom/ZX0kojIVU1+YzOjTFg/4uegwFDDXp0KmVbOcMWywWrly5QlJSEvfu3eP69essLy/z61//mtbW1rjmku1H7HY7t2/f5tq1a0xNTVFYWMhHH31EW1tbTMQAYpUOnVFHrl6FVCZFnJyHpeYwRwuTCJTkoPP8F7f6vuHR15kodEZKdLmo1fGJJoyjkCOAk42oCKvcQkFGLhVZ0h94PWlILi2jsKif1MdTrA4NMLzcQlmmktS/XTOJRILFYuHjjz9Go9Fw7do1ent7CYfDsdDO/RbkEg8CgQAjIyO0t7fz8OFD1tbWqKio4PLly7z//vvfe3uJ5FrUBiM52VkYM+UI2UUUVx+iskAGlWYMM3eYGBzg0cgoA+M2nCdz4Jcn5DCwQVS6RVirQaHRoBXD9yMixKBNQ6XTkCaZYcWxzspakM0A8J3agSaTiYsXL2Iymbh+/TpdXV0sLi5it9s5d+4cBQUFv1ib2ev1MjAwwJ/+9CcePXqEXC7nzJkznDt3jsrKyn9oggl/+68ghImEgoAMwj58IYGoVIlCrUSllCKNk1kBcRVyFNhCkAQQK5KQJiUh+zF3mUyBRCFDJQ0hDvnY2orgi3z/10QiUSyPTKlUkpKSQm9vL7du3WJmZobjx4/T3Ny8492c9jtjY2M8fPiQx48fMzMzg8lkoqWlhXPnzr2SSfN9ohAViEQjEA0S9ntwri+yqg3hnOjgQd8ms9EiimpraarOIE0ev0kijkIWAwqISIn6X/YvDv3gFqgIImGEUISgIEOUpECllCD/B28wuVxOW1sbhYWF3L59m9u3b/Ps2TPsdjsOh4OmpiYyMzP3VWD4ThONRtnc3GRycpJHjx5x//59VlZWqK2t5dNPP+Xw4cM/o26HCBAhEoFICBLxrmGb7aVnfYGJJ910LKQQKWvhzPlWztRlolP8ImdkKZCOOKQEhwvvlgdHFAJ817yIgtdNwBPEHdUi1qaTYZSR9hMZNmKxmKysLM6dO4fBYKC7u5uRkRF+//vf8+jRI86ePcuJEycObIyy1Wrl5s2btLe3Y7PZMBgMtLW1cfToUWpqan5++r5IhEgkQiREEHwruBYcdKzM0NvlJlpxniO/+oQLh7IoSxMRz6SnOApZAqSRhogs3zRby0ZGViKUWMS82gEvQGBmhqU5O87UQtLLqig3KTH8zJHn5OTESgzcuXOHBw8eMD4+TjQajdU7zsrK2tFK+fFidXWV5eVl5ufnGR4epqurK7aFf/78eU6dOvUGqfsv9/EEkRSJQo0qRYPCLkYWieCVqpGmpJOWKiPeTs44u9+SyNNCi3Gd545ZBnqXqUnOJfNbJqzgXmJ6YJrJNVBWHqKypYGqNAWvWw5k26tRV1cXq8vwP//zP6SmptLQ0MDp06dfqZH2LhGJRJibm6OzszPWTzAYDFJYWMiFCxeoq6sjPz//H6b6/zgCggCCWIEsvZTs2mqaKjTovdf582QH7VfNFGhb0ZenEs9pIO4bIrklZi5eqEI85GH+6Q0e+srxlWWSoZWg8G9gnx+kZ1qKzdhGS0sbR5vM5KhEvK6TRyKRkJWVRVZWFiaTidTUVLq6ulhdXWV0dJSVlRXu3btHfn4+hYWFFBQUkJOTs28DZrYr0Y+NjTE3N8f8/Dw2mw2v14ter8dsNnPkyBGOHTv2FotbCUikJEkliCVyJEoDupwqqjKUaD3LTP6/j7j/4H+5kalFq23jbFb8Kv7E/S6lFpXRqPoYQfuEJ32jrPWv8M1KOqlSP5HNVewe8KrryG8+zLHDRVSbRMjeck1RUFBARkYGp06dYmRkhI6ODp49e0ZXVxc6nY6amhoqKyspLS3FbDaTnJyMTCZDJpORlJS05y68SCRCKBQiGAwSDAax2WzMzMwwPDxMd3c3MzMzRKNRiouLaWtro7m5GYvFglarfYsKmQJCxEfY48HhcOFx+nBvrGGzuwnklGBsvsD5gWkcd4d48eArvlRrSD9voThdgUImJUki2tPAorgLWSRNQ557iNoTKaRkTbO0NM7I4EO6u8cZsqWhqLjA2U/aOHmynJq0nXniRSIRarUatVpNeno6RqMRi8XC5OQka2trsVzAa9eukZKSgtlspqioiIKCAvLy8sjJydmz3UKPx8P8/HwsbNVqtTI/P4/X60WhUMS6QW2vA4qLiyksLHz7N4kQImSfY3lynL7hSeamRKyHLfQNVFGX20S5oZa6D86w4fgT07eu0/4fi0Q2z9N25BCNJdkU6JJQ7OHeSNyF/BINyXn11OSVU72UTnp0iY2pGcY3JQhIkEa2iG7ZsSUlo9Uk7ejqWKPR0NDQQENDAxsbG0xMTPD8+XP6+/uZnp5meXk59tkuSZCRkRErciKXy2NZyHK5HJlMFmvTux20tP0zvHSLbadebf8cCoUIBAIEg0ECgUAsJtjpdGKz2VhbW2N1dTXWlWlra4v09HQKCgpobGykoqKCgoKCna1PLAgI4QABsQ5JRgU1dVHcxjRSxRG2AmFCaEmpOkPzBT+L9m94tODC63Bg2wrgD0fZ65jD/ZchEnXgWRpndriXzo4hBhdCeFMKKahroqGuguoiPUb57tliXq+X9fX1mIC2xWOz2djY2GBjYwOHw4FIJCI9PR29Xo9er4/9nJqaikqlIikpKfbZFja8zFwJhUKEw2EikQh+vx+3243dbmdzcxObzYbNZmNlZQW3241cLn/lPAaDAZPJRGZmJmlpaRiNxlit5x1FiBDxu/FurrFuc2DzCIRlWrQGA3pDGmlKMUmEiLhXWJpeZMUVJaLNINVgwJiqIUUhRrqHtsX+E3KMTdxj3fS9GGdwQwGZZZSV5pCXmYJGLEGlVKBW7b7n0ufzMT8/z8zMDFarFavVyuLiIi6XC4lEEpuRt21omUyGRCJ5ZUYW/c0XC7wyEwuCELN/v20Db8/IEokEvV5Pbm4ueXl55Ofnk5+f/85WDd1N9rGQgYiPgNeHNwhRsRgZXjyeIFuBJLSpWgz6vXH4RCKRV179wWAQl8uFzWbD6XTidDpxOBw4HA7cbjd+v59wOPzKZzvAXyqVIpVKkUgkSCQSkpKSUKlUpKSkkJqailarRavVotPpSE1NRaPRvGK2yOXyfZ0EGi/2t5C/S9SD1+XHE5CgVCtJ1sSvZwW8FPh2Nyq3243L5WJrawu/308kEiESicRMiG0hSySSmKmx/bNSqSQ5OfmVz0HePt8N3i0hJ0jwI/wyYxoTHDgSQk5wIEgIOcGBICHkBAeChJATHAgSQk5wIEgIOcGBICHkBAeChJATHAgSQk5wIEgIOcGBICHkBAeChJATHAgSQk5wIEgIOcGBICHkBAeChJATHAgSQk5wIEgIOcGBICHkBAeChJATHAgSQk5wIEgIOcGBICHkBAeChJATHAgSQk5wIEgIOcGBICHkBAeChJATHAgSQk5wIEgIOcGBICHkBAeChJATHAj+f0mvjnJ9dEfnAAAAAElFTkSuQmCC)
maths-General
maths-
In the following fig. the diameter CD of a Circle is perpendicular to the chord AB. If AB=12 cm and CM = 2 cm. Find radius of Circle.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALcAAACqCAYAAADvJt7aAAAgAElEQVR4nO29aXMUV7qo+1TWPI8qzfMsBBKIGYEBt7GbNnTb7dg7TuzY54fc+0P2hxtxO+JGR0fH8Tm7bYPdNhjMLMQgEAKNaJ5LqnkesvJ+wKrGbtpmkKgqkU9EBQRImW9lPrVq5bvWepdCkiQJGZltiJDvAGRktgpZbpltiyy3zLZFlltm2yLLnTckkLJIEshP9FuDKt8BvLNIElI6QSqTJZUVEARQKiSyYhYRJYJah04roMx3nEWMLHc+SUeJLU0yMzPL5EqMoGTGaDPjtBnRChKKZIRkMktC7cRWWU9DfSnlelDkO+4iQZY7XygEkDJkPMMs3viS/3PNw5DYROueDg7uLMGSDhJfnGJhwcdiyoW1/QiHf/MeR7vLqdXJ/cmXQZY7jyg0RvRGNS5VmIg3wGxGSautkrrmWlyZCAmHDYdtDPX9IcZuevibN4kvdpxPjtRQq5Xb719DljufaCyYSitpaqilusZAubiDHXsOcKS3mTJJQkIiGxhmquL/4X/99Qb/+2KGiMJIZW0JpjoDTrlD/ovI3275Rq1Go9GgUWtQa3To9Hr0goCgVKJUqlA7m2h+7zD79pVTkxxmZeAOfUN+poL5DrzwkeXON6JIWhQRsyKSmCaTSpL8yQ/oESp6aO7pYndFHI13nOHhZWbXxTwFXDzIchc8CsCFwVZKmVONTgrgX1snFErlO7CCR5a7KNAhqPUY9CrUQppUMk46Kbfcv4Ysd1GQREzHicVFRLTojEY0OjkX8GvIchcFXhLBNVbXRVKCA1d5KTaHOt9BFTzyxz/faLXoNSpUKhUCGjQ6A8af/EACaW2Q6ScTjEZKUdfuZm93Dc3lch7w15Bb7nyTTpNMi2QyGUQxQzr9s2xJZJrpq9e5d2eeaV077t37ONhqokGXr4CLB7nlzgOJRIJwKEjY78E7do+p/jGGJ9dZlUwMXtXwVbISSyZFJh4j6Z9g5s4jBpdUqCvKqSyRUHnH8WWMxIwmjEYjer0+32+pIFHIayg3H1EUSafTZDKZn7xisRjhcJhAMETA58G7OMXCaD/jjx5ybzLCcraEkgoXVSV69IoMUiJGMpkiJhrROSupaqijrtJBmUWLzWTCYrVhtVqx2WxYLBYMBgMqleonL7VajVL5bnZhZLk3mXA4zPz8PIuLi6yurrKyssLKygo+n49EIoFSqUSlVqNWKlCIKTLxMNF4gmRWRSCaYtXjQRRTuJ12HBYzSrUByeDEaLFSYtOgJU0yliCRzuQ+QKlUCkmS0Ol0OBwOysrKKC8vp7y8nMrKSiorKzGbzfm+NG8duVvyBkiSRCAQwOfzEQwGWVtbw+Px4PF48Pl8P3lFIhEEQcBqtWK32zE7nTgc1VhtNkwmM2azCc/qCtevXWPd66Ozs5POzk4cDgcSkEomyWTSJJNJotEYwWAQr9eL3+/H6/USCoXIZrOYTCYcDgculwuHw4HT6aSkpISysjKcTmfu/BaLBZVqe9/+7f3utpBMJsP8/DyPHz9mcHCQsbEx5ufnUSgUuN1u3G43LpeL5uZmbLZn3Qej0YhWq0Wr1aLT6dHpdeh0ejRaHVqNisX5ORbmF1Cq1LS0tHDgwAEqKytRAJlMGlEUyWRE0pkMyVSKZCJB4rlXNBolEAgQCAQIBoP4fD5GR0cJBAJIkkRZWRnt7e10dXXR2tpKXV0dWq0235dyy5DlfgVCoRCzs7NMTU0xPT3NysoKwWCQYDBIPB7HbrdTUlJCfX09tbW1lJeXU1FRQXl5ORaL5VePL2Wzz1pyvz/XvSgpKXmlGAOBAMvLyywvL7O4uMjMzAwLCwt4PB6i0Sijo6MsLi5y48YNysvLqa+vp76+nsbGRkwm0+temoJElvtXEEWRVCqFx+NheHiYgYEBBgYGmJycRKPR0NzcTGdnJy0tLTQ0NOB2u9Fqtc9m+mk0qNXql/76T6fTZLNZstnsj6105pXjtdlsmEwmamtrSaefdWMSiQRra2vMzs4yPj7O0NAQQ0NDJBIJqqur2b17N4cOHaKjowOn04lWq0UQij9LLMv9CySTSR48eEB/fz9DQ0Osr68jSRImk4kjR45QVVVFY2MjTU1N1NXV4XA43uh8oiiSzWaRJCknuCRJKBSvtjBhI1PyPDU1NTQ0NORec3NzzM7O4vF4GBgY4OHDh7jdbjo7Ozl8+DDd3d1Fn2WR5X4BwWCQ1dVVnjx5Ql9fHwMDA3g8HkpKSti5cydHjx5lz549VFZWotFo8h3uS2O327Hb7XR3d5NOp1lYWODu3bv09/czMDCQ626tr6+zsrJCW1sbLpcLq9Wa79BfC1nun7G+vs7169e5fPkyQ0NDSJJEXV0dH330ES0tLVRVVVFdXf3KfeFCQ61WU19fj9FopLm5maNHjzI2NsbIyAi3bt3i5s2bdHZ2cvLkSY4ePYrdbs93yK+MLPeP+Hw+Hj9+zL179xgYGGBlZQWtVktnZyfHjh2jt7cXp9OZ7zA3nY3Mzu7du/F4PPT19XH9+nWePHnC8PAw0WiUhYUFenp6aGtrK6pW/J2XW5IkvF4vfX19nDt3jsHBQUwmE++99x6HDh2itbX1WV76HRgEcbvdnDhxgq6uLp4+fUpfXx/379/n888/Z2xsjN/+9rccOXKkaK7FOy13Npvlzp07XL16lYcPHxIMBmlvb6enp4ejR4+ya9eubZE1eBUsFgsWi4Xa2lpcLhdlZWXcu3ePubk5/vznPzM2NsZ7771HV1fXKz/ovm3eWblDoRCPHj3i66+/5u7duyiVSnp7ezl9+jSdnZ1oNJqCv3lbiUKhoKurK/dhv3DhAj/88ANff/01oVCIRCJBR0fHS+Xv88U7KXcwGOTChQucO3eOtbU1duzYwZ49e3L9yu0+LP2yKBQKtFotO3fuRKfTUVlZyc2bN7l16xZzc3P87ne/49ixY2+cAt0q3qm7mM1mmZub4/r161y4cIGVlRW6urr49NNP6enp2dZD0W+CWq2mo6OD5uZmysvL+eqrrxgeHubLL78kEAhw7Ngx6urqCq4L907JPTs7y7fffss333yDJEmcOXOGkydP0tDQIIv9EqjVag4cOIDb7ebcuXPcuHGDzz//HK/Xy9mzZ2lubs53iD/hnZA7nU4zOjrK3//+d/r6+tBqtbz33nucOXOGurq6fIdXVJjN5tyDtkaj4dq1a1y6dIlQKMTp06fZt29fwbTg217uTCbD8PAw3377LVevXsVkMvHpp5/y4YcfYrPZ8h1e0bIxD8XhcPDNN99w6dIl4vE4Op2O9vb2ghi53dZyi6KY6xveunULt9vNmTNninbErZAQBIHy8nJOnTqFWq3mq6++4vbt22SzWT799FMOHz6c7xC3r9zJZJLR0dFcqs/pdHLmzBl+//vfF0Srsl2orq7m448/RqPR8Le//Y3bt28jCAJ6vZ62tra8ru/clnJns1nGx8f5+uuvuXbtGm63m3/7t3/j4MGDsthbgMPh4De/+Q1ArgUXRZF///d/Z//+/XmLa1vKPTMzw9dff82NGzcoKSnh448/5sSJExiNxl//ZZnXwuVycfLkSQRB4K9//Su3b9/GYDBgMBjYsWNHXgbEtp3cs7OzXLp0iRs3bmAwGPjjH//IBx98IIv9FnC73Zw6dYp4PM758+e5desWGo0Gg8GQlzx4YeRsNolQKMTFixf58ssvUSqVnD59mt7eXlnst4jNZuP999/no48+QhAErly5wnfffcfMzMxbj2XbtNzBYJBr165x8eJFQqEQn3zyCWfPnsXlcuU7tHeOqqoqPvzwQ/x+P9999x3ffvstWq02t/r+bbFtWu6BgQH++te/srq6ysmTJ3n//fdlsfNIZWUln376Kb29vXg8Hi5fvsz9+/cJhUJvLYail3sjM3Lp0iVGR0epr6/n7NmztLe35zu0dxqFQkFDQwOnT5+mp6eH+fl5vvzyS8bHx99aDEUv99raGl9//TUDAwM0Njbym9/8hra2NtRqucRvIdDZ2clnn31GRUUFd+7cob+/n0gk8lbOXdRyRyIRHj16xOXLlwkEAhw/fpyjR49iMBjyHZrMj+j1evbu3cuhQ4cwGAzcu3ePmzdvEg6Ht/zcRS33yMgI33//PT7fs/JjR48epaamJt9hyfwMk8nE0aNHOXHiBCsrK3zzzTfMzc1t+XmLVu54PM7Nmze5efMm1dXV/O53v6OhoSHfYcn8C1pbWzl27Bgmk4nR0VGGh4cJBAJbes6ilDuVSjE1NcWDBw8IBoO5NY9yPrtw2Rip7OnpQa1Wc/v2bYaGhrb0nEWZ515ZWaGvrw+v15srZ1aoS51k/oHFYqG3t5fV1VWGhoZwu910dXVt2TrMomy5Jycn+f7770mn0xw7doyOjo58hyTzEqjVanbu3ElnZyfhcJgHDx7w9OlT4vH4lpyvqOSWJIl0Os3Y2Bjj4+M4HA4OHz5MeXl5vkOTeUmsVmuufHIgEKC/v5+VlZUtOVdRyZ1MJhkfH2dychKVSkVzczOtra3yNNYio66ujoMHD6LT6bh79y5TU1Nbcp6ikjsSidDf38/8/DwtLS10d3cXVXkvmWc4HA56e3txu92MjIwwMTFBNpvd9PMUldw+n4+BgQG8Xi+7du2Sh9iLFL1eT0tLC2VlZYTDYebm5vB6vZt+nqKRWxRFFhcXGR8fR5Ikdu3aRXV1db7DknkNFAoFZrOZ2tpa3G43Xq+X8fFxYrHYpp6naOT2+/1MT0+TSCQoKyujvr5+221z8a7R2NjIrl27iEajPHjwYNNb76KQO5PJMDs7y9zcHE6nk/b2djmvvQ2or69nx44dJBIJhoeH8fv9m3r8opBbFEUmJiZYWFigpqaGXbt2ybvmbgPcbjfNzc2Iosj09PS7KXc6nWZubo7l5WVKSkpoaGhAp5M3Py929Hp9busVn8/3bnZLEokECwsLeL1eSkpKqKyslCuxbhNsNltuB7j19XX8fv+mpQWLQu5AIIDf70eSpLe+Dk9ma9nYm6e8vJz19XVmZmZea4vCF1HwcsfjcVZXV5EkCbfbjcPheKeLwm831Go1dXV1VFRU4PP5mJ+fJ51Ob8qxC17uUCiEx+NBr9dTU1NTNPuxyLwcKpWKsrIyHA4H4XCYtbW1d0fuSCSCz+dDpVJRWloqZ0m2GSqVCofDgdVqJRqN4vP53p1uSSQSIRAIoFKpcDqdstzbDEEQcDgcmM1mYrEYgUAAURQ359ibcpQt5PmWW5Z7+6FQKLBarZjNZqLRKH6//92ROxqNEggEUCqVOByObZ3fVigUCIKAQqF4px6atVotJpOJWCxGMBh8d+SOx+NEIhEEQcBsNm/rvWtUKhWSJAHPvq6VSmWeI3p7aDQa0uk08Xj83XmgzGQypFKp3LZx2/mGi6JIIpEgmUwCvFOtt0qlQhCE3P3elGNuylG2EFEUEUURhUKRuwDbjXQ6zfz8PFeuXGFoaAiv18vo6Cjt7e2Ul5f/a8mzYcLrfnzBNBm1GbPLicOkLPyb+gIUCkVuY9vNWlNZ8Nchm82SyWRQKBSo1ept2XKHw2G+/fZb/vSnPzE5OUk2m0WhUNDc3MyuXbtevIwuGyS6MsX0+AyTC1FiaheOhjYaW+qosUKxPZkIgoBarUaSpHdHblEUSafTObm3Y8vt9/u5f/8+9+7dy/3bw4cPmZqaesHDVZJswsPU4CgzM2uENEZUViW69WFGr0zz5NEO9vTuoKvViZ0i6Hf+yPNyx2Ix0un0G9d7LHi5s9ls7gYrlcpt2Q/NZrNYLBasVivBYBCFQoFer39xi51ZITR7h1s/jDHiL6P9o7307pIQxi6yfPc6fVdHWUUFJQc5YBMwFondCoUCpVKJJEmkUikymcwby13wb/35tJgkSblswnbC5XJx5MgR3n//faqqqnC73ezdu5eWlpZ/mv2YXRpldeA6D2d9TAhVmJwVVDprqWrpprUsizN6jyeDj7n1JIx/a8qBbBnPZ4o2oxEr+JZbEITcDRZFkWw2u+363Xa7nSNHjhCLxYjH4wQCAQ4fPkxbW9s/yZ1ammHxyWPmo10kmquxmw1oEcC1g/b2CnaOjzC0usjIaIBgu4UqY3F800mShCiKqFQqdDrdpkxpLviWW6lU5vK/6XR6W7bcAKWlpezdu5eOjg5qamqoqKj4sczY83JKJBNxQsEwkUiMdEbkH5dDh9lsxGbRIUgiyUQCUdz8cglbRTabJZ1O5/aw3IwGrGjkhmc5762ob1EICIKA0+nE6XTmBqtedINVJj1GoxYp6Ce4sIwvuTHJSI1SVCCgwWK3YndZKKZaRdlsllQqhSRJ6PX6TemWFIXcarU69+Y3a2i2EEmn02QymVz369m31PPfVAr0ZTVUt7VSY0ihWBji6eQk0+EI4YiHRR9ElWXUN9Wxo9mNRVc83TdRFHMp380ahS74PrdarUar1SKKYi5FtF0nT2Wz2ZzU/+rhWXB2UrE3yMnpC2Qf3uXxxTTpxWoaHBLRJR1+11F2d3fQ3ajEVkQzFdLpNNlsFpVKtWnl8Qpebr1ej9lsJpPJEAgEckPT7yz6aswtxzj2QRSNbpDbngjehRWMGR1KVztudyt7d9TRZodi2RUom80Sj8fRaDQYjcZNWx9b8HKbTCbsdjvr6+t4vd4tK3dbTCg0ZZR3fcixst00BRUkFGqMeiWCzo7eZKfUri0aseHZtOZwOIzRaMRut787cpvNZhwOBx6Ph/X1dVluAAQU5ipc5iqKfadNSZIIBAKEw2HMZjNOp3PTUr0F/0C5IXcmk2F9fX3T68nJ5BdRFPF6vVvSche83FarFafTSTKZZGlpSZZ7m5HJZFhbW8Pv92M0GnE6ne+O3EajEbfbjSiKrKysEAwG8x1SEfBjtuWND5PdnOP8AplMhsXFRTweD1arlfLy8k3LlhS83EqlktLSUrRaLaFQCK/Xu61z3W+OBFIGMZ0gHo0Ri6VIvdLlkhDTCRKRCLFYkqQosZVXO51OMzs7y8rKCk6nk9ra2ncnFQjP+t0lJSW5klvr6+uUlJRsy+mvm0MGKb6Cb3aGyadLrKZMaOp20tTSQKMN9C+6bEkvyeVRhsaWeOrToHZVU9NUR3WZFucWWhKNRpmfn8fv9+N2uyktLd20+1oUcqtUKmpra5menmZtbY2nT59isVi27WDOm6EABQipNaLz17j9f77lwoiG1L7/yUf/w81/7DNR96LtOn2jLFz5//jf/+sBF30N1Jz6A2dLarC7FZRsYbQb/W1BECgpKdnUrc2LoulTqVS5enIrKyuMjo7Kgzm/iApBZ8DqEtBmV/E8eUDfd7e50T/BbCjJP8/OieD3jPHwdj99Pzxi7KmfiEqH1qHDoFJsmSSBQIC5uTmy2SylpaXY7fZNna9fNHLX1dVRXV3N6uoqIyMjhMPhfIdVwKhRmNy429vpOLyfHU3VuLyT+AZvMbrox/O83VIK0tN41uZ54tMQpIqqsnra22poqDJi1/50XuJmMjc3x8jICHq9no6ODmw226YevyjkFgSBqqoqGhoaiEQiTExMsLa2lu+wChuFgKA3YmzopKJ9B+36dYzzd3k8usqwD3IFy5JhsjMjBH1ego5qKKnFptVh0arQCIot7bfOzMwwPDyMwWBg586dm75bRlHIDc9SgjU1NbhcLqLRKJOTk3Lr/YukIJ0lbazHWt/FwTYdDcIUY4Pj3BmPsnHl0tEAS4+XCPlFXC2VlNWXoFVkySZTpGHLMiUbuyk8ffoUq9XKzp07N32b7KKRG54tx+ru7sZms/H48WNGR0fzHVIBI5KVJNJZOwZLA93d9bRViQTGH/H44STLcRHIEA4HGJ5XEkhYaKrSU1eqRKEAUdzaRSHr6+ssLi4SjUYpKSmhvr5+0zfLLSq5N7bDdrvd3Lt3jwcPHmzbxQtvzjM5M0kBtaGEmv17aO1w4fA8ZnnwMUNLMSLRReK+eaYzpUSMLdRbtVTp0yiAzBa6HYlEePLkCWtra7jdbmpra7ekklhRyW00GtmxYweVlZUsLy8zOjrK2tratl169sZIElI6hUJrQNu0h/r2VrqNqwhLT+h/OM+j4WH8K8ukS6vQ1bVi1+gwiplnv7eFYS0uLnLz5k0ikQj79u2jqalpS85TVHIrFArcbjdNTU3Y7XaWlpZ4+PDhpu+CtW2QJKRsiqygI2vZQWVjJ4daFdgyo9y5+YDvLowxvZDAUuuktqMEo16NIi2ypWYDk5OT3Lp1i0wmw9GjR2W5NxAEgfb2dg4ePEg0GuXixYvMzs7mO6wCREBQqVCpBBQKLVnc2Cvb6D7cQL15idXb33Ph6hKPQhW4yx00VWgw6pWIkoBCIaBUKVGyuYJIkpRL5QaDQSorK7ckS7JB0ckN0NDQwLFjx1Cr1fT19TEyMpLvkAoQCbIiopghnc6QTgH2Kir29dDmzmJbvMucL8mMsQO72Y6DNOpsmlRGJJPNImazZNncRjwajXLr1i3GxsZoaGhg//79uFxbNyO9KOU2mUx0dXVRX19PKBTi/v37jI2Nbdp2E0WPlCQTWGFpdJTRwUGGRp/weHqe1YwFVc1Bmuta2eNS0dBUiq21AZsmC6tTzI2M83R6gpmFScbHZng6F2Q9sXkTp5aWlrh06RKzs7Ps27ePQ4cObWlJ6qKUG56lBQ8cOEB7ezsjIyN88803rKys5DuswkBKkgkFWJ1eZ315lWB4maXAOqsxFSldCzU73ufEB7/hkw93cXiHEZsmRmrNx8JyjKRKgdaSJenzs74YJpCQXjBc/+p4vV7u37/PxMQEBoOB7u5uGhoatrQ8XlFMnHoRKpWKgwcP4vf7+fOf/8z3339Pe3s7LpdrW+++8FIo1CiNtTgbjnNMiNIuunDXuXFo1Ag4cHe9x5GSDuIlFRjdYBU1CPZWKno+4Q+WXg6mLJhqWmhyG3BoNmduSX9/P99++y1qtZpjx47R0tKy5ZXDilZugJqaGt577z0ePnzI4OAgly9fxul0sm/fvnyHll8UetTOFmqcLdTs+ef/VlfUUV1R949/UBmgcjdtlbtpO765oYiiyNzcHJcuXWJsbIyTJ9/n9OnTuN3uzT3RCyhquQHq6ur4+OOPcw8rVquVhoYGnE5nvkOT4VlO++LFi4yMjFJWVsbefXtpbGx6K/Uei7bPvYFOp6O3t5cTJ06gUqm4ceMG33//Pevr6/kO7ZVRqVQolcrcfjgqlaqoSzaHQiFu3LjOuXPnkKQMH576gD27e1Cpnhc7iySKm9Kv/zlF1HJnkZDIpEGhEFApFbm5mFarlQMHDjA/P8/Vq1f54osv0Ov1nDlzpqjkeL6U2kZ5MUmSiuo9bBCJROjv7+fSpcusrq7y3rHDvH/iCOUuMz6Ph9SPQj8rUS2gVGlQ67Ro1GrUSiUqpeKNp9oWidxZYJnQ6hqDo0oUOhc7d5ZgM/wj/IaGBn7/+9/j9Xrp6+vjyy+/RK1W50YzN8p1FSIb+/2srKwQCoWIxWL4/X5WVlZQKpUolcqCjf15NpaHxWIxhoaG+Nvf/sb4xAR79vRw5szHNNWVkPGPMHT1Lg9HfPg0JZQ0N1LlNGIVvSQCa6yEdWSszbTsaqer1cabzPAuErlFCI+yONDPub+ryJTuRVtpocegYuMLTqfT0dXVxalTp1hfX2dgYACfz0dvby9NTU1kMpmCFVwQBLRaLQsLC8zOzrK2tsbY2BhKpRKn04larS74HP7Ge8hkMiwsLNDX18fAwAAdHTv44x//yJEjRxGkNZKRp6wMX+LSX8eZNnex4zM7R7QKhPgy/tlhBofXWRDrGPcmSeoOs7dCjUP9em14ccidzSDOPWX25vfc+0FBqM1Ay+luKquMVP7sRw8ePMj6+jpTU1NcvnyZpaUlOjo60Ov1uUqxhYYgCGg0GrxeL5OTk0QiESRJwufzYTKZUCqVBb3if2PLD7VaTTgcZmRkhMXFRaqqqjhx4gRdXV0oVVqQLGhLnDjdJvQpCbXCjKWmnbodTnZky0k01mJSnOPmjVs8vq4ibq7CeqKOAxWvp2kRyJ0BKcDyYpzZp0EUvmVi3hbuTXppb3RQ+bP57U6nk+PHj7O8vEwsFmNiYoJQKERXVxcNDQ3o9fqCbME3HiCXl5fJZrPYbDZKS0uxWCwIglCwMx83dr5IJpOMjY3x8OFDPB4PbW1tfPLJJ5w69QFO549zRxQGNPZy3FVVVLoXiZfVUNe6g+ZmLQ3UAl3UZCZIPb5A38RD+h4ucHxX1XaWO0A6Ost42IpHu4NddT5M6hmmh6YYrqvi0F49Px/Araqq4j//8z8xm8385S9/we/343K56O3tpaOjA4VCUZD76ywtLSEIAgsLCxw4cIBDhw5RUVFRsA+UG/sVZTIZJicnWVpaIplM0tHRwX/8x3/w4YcfUldX91zaT9r4RVD8OPclnSKdu4MSyYyEKKgRlEpUiiyKN8ijFL7coWWSs6MspW1k297nQEUAy1SA84NDDDc0sryniRrhpzlNpVJJZWUlf/jDH1CpVFy4cIGlpSWePn1KV1cXlZU/78wUBjabjbKyMmKxGDU1NXR0dGzZjLnNZHZ2lkePHrG0tMTOnTs5deoUZ8+epba29mc/+ayYviRlkaQEMd8CS6MPGNY5kaQAqfAy433j3As1UNK2n+b9NdS7X1/Rgpc7vexhZXiFtFBFde8udoth1F9/x42rgyyMNjHkrcfmUmJ7QeNWWVnJZ599hkKh4IsvvuD8+fMkk0l++9vfvnAzpXyzUVw/k8mQTCaJxWIFLXc6nWZ8fJwvvviCc+fOYTAY+OSTT/joo49eIPY/UAgAKZLhNbxzk8yawqiSE4Rm73Pj9gzDvhpqdnawp7OKStfrLz0r8EGcEMtrMcZmBFQaE509jTTtP0pTSyUtTBCdfsLAeJSVX6iN6XQ6+eCDDzh79iw6nY5z587xpz/9ib6+voJ7SNnqIb4AAAvtSURBVHt+u5CNXHehdZ02SCaT9PX18V//9V988cUXmM1mzpw5wwcffEBdXd0v/3IWJFSotCaMdhd2p5sShxmbUYkqHSXuX2VlZY1VX5RY+vVjLKym6+ckH7O0ts7gMuhsHhrWZlgQMoQUapwGL4NLTxm4O8f+6lbajP+63Hp9fT2fffYZSqWSc+fO0d/fTyqVIh6P09PTIw/VvyJra2v09/fzzTffcOfOHVwuF59++imnT5+mqqrqV3//2edVg9ZaRkl9K03tpbRnNIQcelJhEVVmhHujN7l6sZpK2yFcHTaMvHpLXNhyz9wmFEyykpFQzs9huRFhRimS9KQQ7DrSsx5mHg4yfcBFuKYM8y8cyuVy8fHHH2O32/nyyy+5e/cufr+fUCjERx99hMlkemtvq5hZW1vj8uXL/Pd//zeTk5O0t7fzhz/8Iffw+/IoUWkNGKwOrC4rTqEFq6MCK3Hs8SXmzg/z+Fofd/fU09lho4ltJvfynRnS1FO+rxGTVkmpARSCgKqtG4c5zdz5OYYm7jL5tJPpvWXsVP9ydaTy8nI+/PBD1Go158+fZ3x8nL/85S8sLi5y6NAhurq6tnTyfDGTTCZ5+PAhV65c4fbt23i9Xnp6ejh79iwnT558ybqNSkCFSqVCJShRqXXoTBZMGhDQozHpcbU10nFfgy6+xur8CqvBGK+7l0ZBy33hhyiZA04ajx+gvcJEgwIkBQhSM8lZicUHkyxcvc/Q3T1c3dWCrUVDpU6J8hcMN5vNnDp1Crfbzfnz57ly5Qqff/45i4uLJBIJduzYgc1m23a7FL8uoigSiUQYHBzk/Pnz3Lp1C0EQOH78OJ988gnt7e0vP39eSiJmwkRDYSKxKJFIkMC6B2/ISUwtoZAk0lPzTKymiJvLKC2to8Zpxs7riVrQcv+/19ZpccR576gGh9nIP4qTOlDpdJiVAVKrEzz+uxvRWYL9492c7CijTP/LX2F6vZ6enh60Wi1ut5s7d+5w9+5dpqenOXDgACdPnmTPnhdMhH4HGRkZ4cKFC/T39+P3+2lpaaGnp4cjR47Q3d39CkcSkWKr+GZHGR8aZWJxjongIOqr32ENullRR5Ei6ywN32dkRIXYfIwTx47T2+KmhNerV1jQcmuaWzHabBgSCRRJyOX6RZFY2o6jqZvOI0aySS3WuI94NEnyJRMgGo2GPXv20NTURGtrK1999RUPHz7k+++/z01aam1tpaysDKPxRTV/ty/RaJSVlRUmJye5d+9ersbInj17OHv2LPv27XuNZxQJSUyTjipRGquo6RFQKstwSwEyXiXryhDZ0DJLUS2ZioPs3X2Cwyd72Fur5XWfhgpa7v/r//6f2Jw23KU2HM9HqrBgqDjA3j/WUn00jD+lQW0rpbTcRYnu1T7lFouFQ4cOUVZWRn9/P3fu3OHKlSvcuXOHffv2cfr0aXp6et6ZWuDxeJyBgQEuXLjAwMAAmUwmt1J9z549NDY2vubDt4BCX4at/jhH/riT5veTJNCgNRnR6zRoFGlIx4nGs6SVFqyl5ZSVarG+Qe+woOU+0dv54v8QtGgsFZRZKijbhHouVquV7u5uamtrKS8vx2AwMDExweDgIJFIhEePHtHS0kJzc/MvDk4UK5IkMTs7y9TUFCMjI4yOjjI/P49araajo4OTJ0/S29uL2fxL+ahfQ0ChtmBwWahx1VOzadH/awpa7reN3W7n/fffZ9euXTx58oTr16/z4MEDHjx4QFNTE8eOHePAgQNUVVWh1WpRq9VFu3VJNpslnU4Tj8eZm5vj7t273L59m9HRUYxGI/v27ePYsWO0trbicrk2dceDt4Us988wGo0YjUZKS0txOBxUVlYyNjZGKBTi2rVr9PX1UVJSQktLC93d3W/wNZ0/NmbwDQ4OMjExwerqKrFYDKVSyZ49e2htbaWnp4fu7u6iTo3Kcv8L9Ho9hw4doru7m5mZGR48eMDdu3cZGhpibGyMxcVFvF4v09PTVFZWYrFYMBgMmEwmDAbDa0mxFbP/NuaoRKNRotEooVCI1dVVJiYmGBoaYm5uDpVKRXNzMwcPHuTAgQPU1dUV3Lyb16H438EWo9fraW1txWq10tTUxNGjR1laWmJ1dZXh4WFu3bpFOp3G5XLR2NhIe3s7DQ0N1NTUYLfbX+lcG1NIn//7mwjv8XhYXFxkamqK8fFxJicn8Xg8KBQKSkpKKC8vZ/fu3VRWVlJRUUFNTc0rjjIWNrLcL4EgCFRUVFBRUcH+/fsJBoMMDQ1x9+5dxsfHWV5eZn19nXQ6zdraGoODg5jNZiwWC1arNfcyGo3o9fqfvLRaba7frtFoUKlUqNVq9Hr9v+zuZLNZEokE8XiceDxOIpHItc7BYJBgMEggECAUChEOhwmFQrmpBvCsznlHRwc9PT1bWogy38hyvwZWqzWXI49Go/j9fhYXF5mZmWFycpLBwcHcVt5GozH3wXC73TgcDux2e+5Pq9WKyWTCarWysLBAIBAgGo0SCARYXV1FqVSiUCiIx+O5daDxeJxAIIDX68Xv9+f+vrq6yuLiIktLSyQSCaxWK2VlZdTU1NDT00NdXV2uC2UymbBYLNs6h6+QCnVOZZERjUaZmZnh6dOnzM/Ps7S0hNfrJRaLIYpibp2hSqXKvTZWtguCgFqtznV1wuEwVVVVVFZWYjQaUSqVSJKEIAi5JWeZTOYnr3Q6nZsiq1QqMZlMlJaWUl5eTk1NDfX19dTV1W1rmX+OLPcmIkkSoijm5mVvjPTNzs7mHkAjkQiRSIRwOEw4HCYajRKLxUgmk4RCIZaXl4nH4xgMBoxGYy7lqNVq0el06HQ69Ho9RqMRs9mce4C1WCw4nU4qKiqoq6ujrKwMk8mUK/Cz8Q3wLiHL/RbY6DpEIhESicRPXslkklQqRSqVwuPxcOnSJZaWlmhubqa9vT23771arc61+BqN5ieya7XanPA2m23b9qFfFbnP/Raw2+0vlTkJh8OUlZUxOzvL7t272b9//1spGLldkVvuAmNqaopwOIzb7aasrOyd60psJrLcBcSztZPPVogLgiCL/YbIcstsW4pz1o+MzEsgP1AWBFnEyBr+NT+BFCR5tk2eWiUgKLJImTQZpR7BWIrNYsCu5xeX0sk8Q5Y774iQmGfhwW3u3RvnaUxH1urCZdViUkukw16i64uE1JWomj9md1cjh6tBXuL568hy5xWJ5Npjlh9c4dKtWQa9ZowVNursNhxWLXplllQ2jGJhlqXVAMuqw1grGtlXATpZ7l9FljtvSJBdZeXhJX74/O9cDLSi7v0tJ040c7xWg1KpQEBCintIVEVxjoe4jQJVRkKS5D7JyyDLnS/EMHgeMHH3PpfuR1hpr+b4gZ10thuxP188y2TArDlCp9VHet2GzZRBrVDxeuvB3y1kufNF0kvqaT+jo/M8jtdRVd/O/g4jpf9UFU4B1nZKmpL0OLWo1Vk0cpfkpZDlzhNSPIx3fpZFT4iAbidtThflRl5QxkAAbOiNWco0EgoJlILcar8Mstx5QkomCfpChBJpskYjOoMWA7808CCg+te1PmVegDyIky9+nIoqKBQgiohidkv2YnyXkeXOEwqtDpvDik2rRAiHiEbihIDC3rOsuJDlzhMKvRV7Qyt1VXZKU/P4ZqcZns/gfdEPS0kyiQiRSJJYUiIrzwZ6KWS584XGgar5EB27G+lxLJF4+oAbt2aZ+Ce7JQjOsD43wpNpD1PraVJy/+WlkB8o84VgANsOGg8d57crIdJPllm9fp7LyTbiTTZMei16jQqVIKGIegillMSMWd6NioWbgzzlNc+IiUXCT+/Q98NNrg4sMp8yonGUUVJiw201YDRZ0VnLKa2qpaWhnDKrDoNGQM4G/jqy3AWBn8DofYYGRhheTRNS2bDaTNiMWnQGC1p7NeUVlTRX6NHLAzgvjSx3oSBlEFNp0qKEiALhuYpTCkH5bNNR+QnplZDlltm2yG2BzLZFlltm2yLLLbNtkeWW2bbIcstsW2S5ZbYtstwy2xZZbpltiyy3zLZFlltm2yLLLbNtkeWW2bbIcstsW2S5ZbYt/z8N+m2NZMe8yQAAAABJRU5ErkJggg==)
In the following fig. the diameter CD of a Circle is perpendicular to the chord AB. If AB=12 cm and CM = 2 cm. Find radius of Circle.
![](data:image/png;base64,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)
maths-General
maths-
ABC is an equilateral triangle of side 6 cm, a Circle with centre ‘O’ passes through the verticles ABC. Find radius of Circle
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)
ABC is an equilateral triangle of side 6 cm, a Circle with centre ‘O’ passes through the verticles ABC. Find radius of Circle
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)
maths-General
maths-
From the fig. segments shown are tangents then x =
![](data:image/png;base64,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)
From the fig. segments shown are tangents then x =
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPkAAAEPCAYAAACA82IgAAAgAElEQVR4nOydd3Ob55W3L3SAKCRIVFawd4qkWMSmXiyXxLHXmc1Odmf2m+ST7GyZTbKvHcVFjiyrUZQlURR7EXtvIFhQCBAg6vuHQ8ROnNiSWKHnmuHYI4nPc/AAP5z7PvcpolgsFkNAQCBhER+1AQICAgeLIHIBgQRHELmAQIIjiFxAIMERRC4gkOAIIhcQSHAEkQsIJDiCyAUEEhxB5AICCY4gcgGBBEcQuYBAgiOIXEAgwRFELiCQ4AgiFxBIcASRCwgkOILIBQQSHEHkAgIJjiByAYEERxC5gECCI4hcQCDBEUQuIJDgCCIXEEhwBJELCCQ40qM24MCI+ImEIwREKiQSCUrJURskIHA0JKDII0S211ibmGDVLyeSWY7FkkyWBERHbZqAwBGQgCLfYHvhCY/+cI8+rxX9Oxm06ZPJVAoiF3gzSbA9eRj/5izTXY/oethO58A4E+t+3GEQZkEJvKkkkMhjxEJrrEzMMzLswBUIIdPIkMh+ov+OxYQvAoGEJHGW69tr+Ff7WdrYYUmRg0o/T4ZOiloq+sduPOIm4FhkYc2PCz1aczaZFjlaEYAX33aY7YAUtXwXWcSDY30XrziF1AwLliQguMHW8jrrfimitAyMqUnoZfv/8txuN4uLi+zs7GAwGLDZbIjFCfQdLXBgJIDIY0CQndUZ5l8s4FRa0VaeIn1xnK1IGFEsSpQf0HksRDS4zbZ9kZWFOeYdblY9UkTaFdZKCynMkJDkmmRqzs2UR481FazSNean7cwHDGgLT1FmU2Pyz7A0Oc6LFfCllFFQVsLpohRS5KLXXibFYjG8Xi+rq6uMjo4yOTnJ1tYWZrOZqqoqiouL0Wq1qNXqQxR8jFg0SjQSJYoIsVSKZG+xFAkTiUSJiiWIJRLEIiEOchxIAJHvgG+KpdVV+tbTUFfmcCptjXm9FJcDon9vMrNzgs25UTqnRWxJDGRZVBidnQx8fZvhsTOkl+eSt/GY6bFFnmznk5WXTbPVQ3R1hMm5ALO9kzzPyaLO6kcWnmdufJ3x5RmmFjyIU9uoTk8i7TVfmd1u58GDB3R0dLC6uopEIsHlcuH1erl58yZlZWU0NjbS3NyMzWZ7zbv9RKK7hL1ONu3ruHbliA1ZmKxqUgjiW53Hse4nlGZFazFikMMBLGoEXpITLvIIoR0nvrl5Vr0yYrbTFBVZyfG7CKhiDEpkSBQqFMrvvtAYxPy4p4cYffKM3kAVSQ3NNJSJ0ISncQ4OsL7jYWPTg3FlFvv0JIPbGnb1BbQWmzDJZ9HNTDP7fBu7I4LlvQIq07MxL9l50d7NlEjL0OV6MixJpL2ic11aWmJ2dpaBgQF6e3uZn59Hq9Wi1+txuVwsLy+zvr5OMBjE7XYzPz9PSUkJNpuNzMxMjEbjPj3fHyDsJ7Axw3L/c4YcUtyZrZSUZlIhmWZ9YIDhVQni8mYKdUZ0gsiPBSdY5DHAy/b6CkN9W9gxY21OIz1ZAZ4gwUCYcDiCOBQkHIIoe1HGKMQczI3PM9C9wU6VkpxCIykpIgzFLbR+aCFDnodMuoslKY2NVRcKaTYWWwV1TUnoYmFcSy66+oNIkq1kNzZRmRbCvOti/fEsoyEnLncYTxBQvvyrmpub4+uvv+bBgwfY7XZsNhvvv/8+RUVFOJ1O7ty5g1gsprq6mrS0NEZGRrhx4wZyuZzy8nIuXbpEQ0MDNpsNkegAFsvRMGHvFj77IFMjO/RNyZlfXCGqHcM5P8OIP4OUjCAZQYjGENbrx4ATLPIohFZwz3fT2d7DhEeBdW2SUZ2CwMogE/3TjDuXkdy+gZxrqBsqKbdKSZWGIebAseJgdm6XWHUSKQYpShHILJXkWirIQIzcNQ07OlINaahDZtJMVnIsOkSskG4xY0pyI9KnYcrLIV0GygwLmalylggRDkYJRV7u1UxMTNDb28vAwABTU1MEg0FKS0tpbW3l7NmzWK1WBgcH6e7uBuDy5cvk5eWRkZGBRqNhfn6e+fl5/vjHP/LkyRMKCwspLy+ntLQUi8Wyf49drESeYsVclEWmY4Rnfd28WHeSVa/HmnuKMrkFXXYaZoXgxY8LJ1jkMQj5IOAkuGtnaXKD6bVRxAox4e1NXIurbGzHkIoeIjfayMwuI9MoJVUaA1EEsWiHUNCFa82J3Q5+G+gRAVHCoRhR7w6KYOjPAbsYsWiECGGkRIjEICYSISJKLBwhIhMRicSIIkIkFiERw09xopFIhJ2dHaanp+no6KC9vZ3V1VXy8vL42c9+RmNjIxkZGSQlJREMBtnd3WV3d5doNEpSUhIFBQWkp6dz/vx5xsfH6enp4cmTJ9y7d4+nT59SV1dHc3Mz1dXV8esoFIrXe+wyNar0cvKMuwTDEcZ7+hnf1OPKeJvGczlUqqWIpXLkMpAKXvxYcIJFLgapBX1eC+c+yCarwYUvEiEsjrCzNs5ER5gppwLJ6RYqTxVQbpKgkwBIQaQnJVmMRrbE0ItBerqWOG3MJF3tB/cMM0sq/Bt+Cnwgk0qQSMSIEP155SkCsQiRSIxYJEIs+nZNGhOJEYnESCQSJFIJPyXYPTIyQnt7Oz09PbhcLvR6PVVVVdTW1lJXV0d6enr830YiEcLhMJFIhGg0ikgkQiwWo9Fo0Gg0mM1m0tPTyc7OZnR0lIWFBZaXl/nv//7v7wXpampqMJlMr/7YRWLEUhViqQ2z1YpV8pylUJBoihGVSYf21a8scECcbJHLM0kpyORsAZyN/3kI5/gtbjvmUK6lIb7yIW0XS2kzwLc1KlIQWbAWFlJe0c3A8ADDn/+OL3ZqcOUGkfm2sMfyUUT8aDbdbNjXcK3b2XQ5cfhipIS3cK2tsbnlJbblwrGxjSstxPaWnY3NdVbYhDUXO740UP6t0gOBAKurq0xOTtLV1UVnZydut5vS0lLeeecdmpubfzBwFvvzKcHePjsS+f5+QKFQUF5eTnl5OW63m5GRETo6Onj06BHj4+Osra2xurrK9PQ0paWlZGdnYzAYSE5OfrXHHw7j2wqhUEZRJcXYDYVwe4GkCIhFxBAL2/FjwgkW+d9DhlqlRCmTIpPJECuVyBV7At9Di6GihQbPBgv+b7jd9998PnqTB+nF5JfX0HBeySmDG8+cm7mZJTyeGdY3lphcCZHjW2FtYYktt5/A1iZzs2usxFz4VmdZdW2w4N+A2RW8W1mQ9v3IWzgcZmhoiK+++oquri5CoRA2m41f/OIXVFRUUFBQQFra6x68QXJyMjU1NRiNRhoaGpicnGRsbIzR0VF6enrQ6/WcPn2alpYW6uvrX8GzR9he8uBc9qJODaIUB3E4vCzP7OLO9KNNVhGRKJAixN2OAwko8jAhmRFr/UXqtjWIrApMfDe6DiBBbqwgv1nE9UgyqpReBlfCuLUZmDKLKbBZyU+V4HGeofSMlfdDuWQV6lBKFEik2WSUtXCREIGsAnJUchRiBeL0csovSxEHMjHadGQm/eXR+nw+xsbGGBgYYHBwkJmZGQCqqqq4cOECbW1taDSafX0KKpWKwsJCCgsLOXPmDP39/Tx8+JCBgQEcDge9vb0sLS3x/PlziouLKSgooKCgAL1e/8MXDLoJO6aYnF9jeluG16dEJzJjKzayuOCg49k3PPHtknveRIU6iSShtPfYkIAil6AyllD5fhbFUTGotCiVP5Skr0JiqKL8io3sxo/w7UYJiVUo1FqSdUqSpCnoW9L5sDrIu8iRqZJIUkqQRc0kWxuo2o0Rk6lQqpUoZRbQZZFxKkQQObIkLUkqKZFIBK/XS19fH3fu3OHp06dEo1Fqamq4ePEilZWVGI1G1Gr1gT6RpKQkamtrKSgoYH19ndHRUZ4+fUpfXx99fX2YTCZqa2tpa2ujuroas9mMVCpFIvmOUkMeIoudDD8c5Ct7BqqiS1yvrqM0x8Wmt4fn/cPYkw0s7ljJi8rQInjx40ICilyEWKoiSa8i6Uf/qRy51kCa1vAD2WlSJFolir+JJCmQq34gwCRLQvmdPwwFfLQ/7uTp06eMjo4SCATIzs6mrKyMhoYG6urq9t17/yOUSiVKpRKTyURWVhZms5n8/HzGxsZYXl5maGiIyclJrFYr5eXlVFdXU11d/Rcbk7TI0rIx5oYp0VlIKc6koCgVszhKVdjIe3rAbCXXpEElFQkCP0YkoMiPFp/Pi311lcHBIdofPqSvrw+pVEpraytXrlyhtrb2wD33j6HT6Whra6OlpYXV1VV6enp4+GdbZ2dnmZqaYnZ2luXlZUpKSjAajej1GlSFF2jJvkhlQIZcIUerAqjA1lzAR1UxpAolWq0SiVA3c6wQRL6PuN1uOjo6uHfvHuPj4ygUCurr66mtraWyspKCggKSkn50fXFoiMViMjIyUKlUZGRk0NzczPj4OOPj4wwODvLs2TPS09Opqanh/IXzVNfUoFIq/yqeqECVpEB1fF6WwF8hiHwfcDgcTExMMDg4GA9oKZVKGhsb4977OJeFpqamkpqayunTp1lbW6Oz89ttRn9/P0tLS/h8Puxra/T09FFcVIjNlkN2djYKxSvk7QocOoLIX4NYLMbq6iqPHz/m9u3bjI6OkpyczLlz52hqaqKwsBCDwXCsBf7XmM1mLly4QHV1NQsLC4yMjHwboOvtpf1BO1lZmbS1tdLWdpbS0lJSUlIOJkdeYN8QRP6KLC0t0dnZSU9PD3NzcwQCAUpLS6mpqeHcuXNUVFQctYmvjE6nQ6fTkZOTQ0FBATk5OWRlZTE2Nsbm5iZPnjxlcHCI7OxsysvLqa2tpaioCKlU+DgdR4R35SWIRqN4PB6WlpZ49uwZd+/eZXZ2FovFwqVLlzh//jwFBQWvnx9+jLBarRgMBlpaWlhcXIznx/f09DA4OMjo6CjLy8vxIzq9Xo9GoxEEf4wQ3omXYH5+nvv37/P48WPsdjtqtZqrV69SXV1NVVUVBQUFR23igSCTyZDJZJSXl5OamorNZqOmpoapqSmWlpa4c+cOd+7cwWaz0dTUxJkzZygtLT1R25RERhD5jxCJRFhaWoqXgvb29rK2tkZGRgbnzp3j6tWrh9eV5RhgtVqxWq20tbUxOztLZ2cn7e3tvHjxguHhYba3t5mdnaW0tJSCggIyMjKwWCyCZz9ChCf/D4jFYkxMTHD37l3u3r3L+vo6eXl5/PKXv6S2thabzYbZbD5qM48EkUhEbm4uOp2OU6dOMTs7y4sXLxgcHOT27dvcvn2bkpISWltbaWpqoqioCKVSiMYfBYLIf4BIJMKLFy/o6emhv7+f5eVlIpEINTU1tLS0cP78+e+Vgb6piEQiDAYDBoOB8vJyysrK4u2nZmZmWF9f59atW/T19VFQUEBZWRklJSXk5eUdtelvFILIv0M4HGZ7e5vx8XHu379Pe3s7brebqqoqPvzwQxobGzGZTMcqoeU4sbeyuXTpEjMzMzx//pyOjg6ePXtGd3c3paWlnDlzhvr6evLy8lCr1SiVSuEI7oARRP5notEovb29tLe309vby/b2NiaTiXPnzlFfX091dfXrNVt4AxCLxajVatRqNSaTCaPRSFZWFhMTE8zMzLC6usqnn37K3bt3KS4upqamhoaGBnJzc4/a9ITmjRe5z+djeXmZsbExnjx5wuDgIF6vl8rKSt566y1aWlpITU09ajNPHCKRKF6+6vf7GRsb4+HDh3R2djI9Pc3a2hqLi4ssLi5SUVFBdnY2JpMJg8Fw1KYnHG+0yAOBAH19fdy6dYuuri7C4TAVFRWcPn2aU6dOkZOTIwh8H1CpVJSXl6PX62lsbGRiYoKRkRHGxsb4wx/+wJdffklpaWm8aCY7O/uoTU4o3kiRu91uhoeHGRgYYHh4mMXFRRQKBadPn+bKlSs0NTUJ++59Ri6XY7PZsNls1NXVMTQ0xJMnT+jr62Nubo6xsTGcTieDg4MUFhZSUFBAcXHxG3t6sZ+8USIPh8Nsbm7S09PDn/70J/r6+pDL5TQ1NXH27FkqKyvR6/WCwA8YmUxGRUUFNpuNt956i7GxMbq6uujv7+fLL79ErVZz6tQpzp8/T21tLZmZmcjlcuGs/RV5Y56a0+mks7OTx48fMzExgdfrpbCwkMrKSpqbm6mpqRHOcQ8RuVwer37LyMggPT2dgoICBgcHWVhYYHFxkd/+9rfcvn2boqIi6uvrqamp2ZceeG8aCS9yp9PJysoKfX19PHr0iBcvXqBSqWhqauL69etUVlYeeROHNx2VSkVtbS01NTVsbGzEl/J7OfITExMsLy+zsLBAaWkpGRkZpKamHmpnnZNMQot8fX2d9vZ2vv76a6amptBoNLS2tlJTU0NZWRkFBQWC9z5GiESieIdZq9VKTU0N4+PjTE5OMjc3R09PD6mpqdTW1nLu3DnBs/9EElLkKysrTE1NMTAwwMjICEtLS5jNZpqbm7l+/TqFhYVHbaLAP0Cj0VBaWhqPuA8MDPDo0SOePXvG+vo6z58/Z21tjd7eXoqKisjPzycnJwedTnfUph9LEkrksViMhYUFHj58yK1bt5iZmYmPEWpubiYvL084hz1h6HQ6GhsbKSoq4u2332ZsbIze3l56enro6urCZDLR1NRES0sLlZWVmM1mofrtr0gYkc/Pz8dH/Y6Pj7O8vIxarcZoNMaFvVdNFg6HEYlESKXfDmBQKpXx0cApKSnIZMKovuOEXC7HbDZjNpvjZb1lZWW8ePECu93O5OQk8/PzWCwWSktLKSsro7S0VNiz/5kTLXKv14vX62VpaYn29nZu3brF6OgoOp2O8vJy8vPzSUpKYmVlhcXFRUKhEOFwmFgshkQiiddJq1QqdDpdPNqbmpqKVqtFoVCgUChQKpWoVCrhCGcfiMViBINBwuEwoVAo/p58d85bLBYjHA6zu7tLKBQCiL8Xe+/bmTNnyMvLY2RkhMePH9PT04Pf76egoID6+nocDgclJSWkpqaiVquRy+VH/MqPjhP7qV1dXeXp06d0dXXx4sULXrx4wfT0NPBtACcQCBAMBpHL5fEPEXybXx2LxYhGo+zs7BCNRllfXycQCMR/dnd3UalUWCwWcnNzyc3NpbCwEJvNhkqlOsqXfeJZW1tjZWWFjY0N1tfX2dzcZGNjg62tLbxeLzs7O/EJrqFQKD7zbU/cKpUKrVaLVqtFIpHEvzAyMzPj//7Zs2cMDQ2Rnp5OWVkZ9fX1nDp16o0Nsp4YkUejURwOBw6Hg8XFRQYHB+no6GBkZIRgMEhKSgpNTU2YTKZ4cYTBYECn06FSqeLJFFKpNO4pgsEgwWAQr9fL1tYWDoeDtbU1dnZ2cLvdbG9vs7W1xdzcHIODg1itVnJycsjMzMRisZCSknLUj+VYs7m5ydbWFi6XC5fLFRe0x+PB5/PFV2J74vb7/QSDwbiHh2+/sEUiUdzDS6VSFArF36zAsrKyCIVCLCws0Nvby/z8PAqFgoqKCiYnJ5mYmKCoqAiz2YzVak2oFl0/xokQeTgcZmJigsePH/P48WOGh4fZ2NjA5/NhNpupr6+nubmZoqIi0tLS4svwvT23WPztSOG9cb+xWCzuzaPRaFzw3/XkLpcLu93O8vIyi4uL8bJTs9lMbW1tfAywUFf+t+zu7rK0tMSLFy8YHR1lamqK6elpvF4vycnJGAwG0tLS0Ov15OTkkJycjFarRaVSIZPJ4u/T3qgmkUgUH928955FIhGCwSA7Oztsb2/j8XjY2NhALBYjk8niy/OFhQWcTif379+Pt6e6ePEiFRUVb8ye/ViL3O/3Mzo6ysDAAP39/XR2djI0NARAeXk5Fy5coKqqKl5Q8spjeP8O6+vrzM7OMjMzg8lkYm5uDrfbTX9/P1NTUzx+/JjTp09TU1PzxjdCcLlczMzMMD09zczMDA6HA7/fz+7uLsFgEIPBQHZ2drx91N5qKy0tjbS0NFJSUlCr1S9VWx4IBHC5XPGlv9PppLCwkOrqapxOJ263G4fDwczMDGNjYwwPDzM8PMyLFy9oa2vj3LlzlJSUHOBTOR4cS5GHQiFcLhdDQ0N89tln3Lt3D7vdDoDBYODMmTP8/Oc/jy/P95Zv+43RaCQlJYWKigquXbvGxsZGfO53f38/o6OjTE5OYrfbOXv2LDk5OWg0mjfmCCccDrOzs8Pq6mr8y3h4eJjZ2VnkcjlFRUWUlpaSl5dHbm4uZrMZtVod3zZJJJL4z6s0jlAqlZjNZgwGA4WFhd/z8ntz4KenpxkeHqarq4uxsTFcLhcPHjxgfn4ep9PJu+++S2ZmJmq1OmFPVUSxven2x4RIJEJnZyfffPMNz58/55tvvmFtbQ2j0UhbWxvNzc3U1dVRWVl5JGWgTqeT0dFRxsfHefHiRdy7p6en09LSwoULFw6ka6vP56Ovr4/f/e53eL1e/v3f/53z58/v+31+KpFIhL6+Pjo6Oujt7cXpdCKTyTAYDBiNRjIyMuL92q1W65FVk21tbbG2tsbS0hJLS0tMTk4yPj7O4uIiAHl5eVRXV3Pu3DlOnz6dkFH4Y+XJ7XY7PT09fPbZZzx48IC1tTUUCgWNjY20trZy9epVzpw5c6SZTXq9nubmZpqbm5mdnaW9vZ27d+8yOTmJx+PB5XJx9uxZCgoKEjLl0uPxsLKywujoKF1dXfT29rKxsYHZbKa4uJjW1lZOnz59bGIVe0eipaWlwLfR/aGhIbq6unj27BkzMzM4nU5cLheLi4uUlpaSnp6eUO/dsRH5wsICn332GZ9++ilDQ0P4fD4sFgsXLlzg2rVrVFVVkZ6ejlb7N0ODj4zc3FwUCgVlZWV0dXXxzTff8PnnnzMyMsLbb7/NlStX0Ov1R23mvrG9vc2zZ8+4c+cOPT09hMNhcnNzeffddyktLY3vt49zo429LUNeXh5nz56ND3fs7+/nyZMnFBcXc+3aNdra2hKmlv3IRe71ehkaGuL27dt88sknjIyMkJ6ezvXr16mrq6OtrY36+vpju4xKT08nPT0dm81GcnIyt27dYnJykt/+9resr69z9erVE58rHwgEGBkZobOzk/7+fhwOBxqNhuLiYlpaWmhrazvWwv5rNBoNGo2GvLy8+OSXBw8e0NfXx9TUFDs7O0xOTtLc3ExVVdWJ/6KW/OY3v/nNUdw4Fovhcrl4+vQpv/vd77hx4wYrKyvYbDY+/PBD/vVf/5WrV6+Sn59/bAX+XTQaDbm5uWRmZhIMBunv72dsbAyJRILJZHrtwYChUAi73c7w8DDBYJCampoDH+oQi8Xw+Xz09vby+eefc/v2bbxeL01NTfzyl7+Me/D9PtU4TGQyGRaLhYqKCkpKShCLxUxNTcWHaCiVynhw96R2lT0yTz41NcW9e/e4efMmXV1diMVi3nrrLS5fvkxjYyMVFRUnLtqp0+lobm6Op8A+evSITz/9FI/Hw0cffUR5eflRm/hSTE1N0d7eHg9+5uTk0NDQQFNTE1VVVQmT5qtUKrFYLJjNZlJSUjCbzTx58oSZmRn+4z/+g9HRUa5du8apU6dOpNCP5F3a3Nzk66+/5n//93+ZmZnBbDZz8eJFPvzwQ86cOXMiPPffQyaTUV9fj9FoxGQy8emnn3Lnzh1kMhnRaJTS0tJjL46dnR2mpqa4ffs2jx49YnNzk7q6On7xi19w5syZhE0PFYlEVFZWUlRUREVFBV988QUdHR3cvHkTn8+Hx+OhqqrqxGU6Hvpy3eVy8eTJEz7++GOmp6c5ffo0v/71r3nvvfeoqqpKiA+QSCRCr9djNBrRaDQsLy8zMDCA3+8nKyuL1NTUl/YIh7Vcj8ViPH36lP/5n/+ho6MDnU7H5cuXef/996mqqnoj+t9JpVKMRiMWiwWDwcDm5iYDAwPMzs6iUChO3ICNQ3Up29vbtLe388c//pGNjQ0uX77Mz372My5cuJCQKYZ5eXno9XokEgn/93//R3t7OzKZjF/84hfHcn755uYmnZ2dfPHFFwwNDWEymXjnnXe4evUqmZmZR23eoaJUKjl16lS8B8EXX3zB+Pg4H3/8MW63mwsXLpyYQZeHJvLt7W2eP3/Op59+yvDwMGfOnOHf/u3fKC8vT0iB76HX67l69SpisZjf//73fPnll8jlcjQaDTk5Ocdmj+dyufjmm2/47W9/y9zcHKdPn+add96hoaHhjW60odVquXTpEhkZGdy4cYMnT57wySef4Pf7effdd09Ej/hDWa6HQiG6urr43//9XwYGBqioqOCjjz7i7Nmzb0Q1kE6nw2Kx4Pf7mZ6eZmpqilAoRHZ29k+OTB/kcn11dZUvvviCGzduYLfbqaur4/333+fs2bOvfSqQCCiVSjIzM9HpdIRCIebm5piammJ7exutVovFYjlqE/8hB+7JI5EIw8PD3Lx5k+7ubvLz8/n1r39NS0vLG/XhsVgs/PznPwfg97//PTdv3sRsNvPuu+8e6Rnz0tIS9+7d49NPP2VjY4NLly7x0UcfUVxc/EZ8Ab8MDQ0N8XqGW7ducevWLcLhMFqtluzs7GMbUD1wT2632/ntb3/L/fv3SU9P58MPP+TChQvHKnPtsEhJSUGj0eB0OpmZmcFut6PVaikqKvrRopaD8OROp5Nbt27x8ccfEwgEeOutt/jZz352Io8vD4O9gKrBYEAsFrO4uMjc3ByhUAiTyXRsU2EP9KtnfX2dBw8e0NHRgVQq5d133+Xq1asn7ghivxCJRBQXF/Phhx8SDAZ59OgRf/rTn7DZbJSWlh5q15mNjQ3u3r3LrVu38Pl8XLlyhX/5l38hJyfn0Gw4qRQWFqJUKlEoFHzxxRfcuXMn3rHGarUetXl/w4GJPBqNxnO5o9Eoly5dSqh84FdFLpdTXV3N5uYmq6urTExM8MUXXyCVSqmqqjoUG3w+H52dnXzyySdsbm7yzjvv8N57752IINJxITMzk/feew+fz8fXX3/NgwcPUKvVXL9+/diNuD6QwudgMMj09DSPHoJc7q8AACAASURBVD1iamqKyspKfv7zn5Ofn38QtztxqFQqGhsbef/999FqtTx48IDnz5/j9XoP/N6BQIB79+7xhz/8AbfbTWtrK++99x4lJSVvVIzkdRGJRKSnp/PWW29x8eJFPB4PX331FU+ePGFzc/OozfseByLy1dVV7t27x9TUFHl5eVy6dIlTp06d6Ey2/cZoNHLt2jWam5sJhUJ0d3fHE2YOilAoxMDAADdv3mR2dpa2tjZ+9atfHUj9+5tCcXEx77//Pg0NDTidTu7evcvz588JBAJHbVqcA1muj42Nxfd6b7/9NmfOnEEikRzErU40BoOBixcvsra2xujoKH/6059IT08nNzf3QO43MDDAxx9/zNLSEvX19Vy7do3S0lLBg78GEomEwsJCPvjgg3jDE6lUSnZ2drzg5ajZV5FHo1Hsdjvd3d0sLCxQW1vL+fPnj/054lFSWVnJ1tYWMzMzdHd3c+bMGUwm074OYYxGo6ytrXH37l16e3spKyvjo48+orKyUhD4PiASiaipqcHv97O2tsbExARfffUVUqmUoqKiozZvf5frHo+HBw8eMDAwQEZGBmfOnBGCOT+CRqOhsrKSU6dOIRaLef78OSMjI/E+8fuBw+Hg1q1b9Pb2YjabaW1tpbKyUughv89UVVXxwQcfYDAYuH37Nvfv3z+UOMuPsa8iX1lZ4e7duywuLtLc3Exra+uJSuQ/KiwWC9euXaOoqIju7m4ePXq0b3vz7e1tent7uX37Nn6/n8uXL9PU1CQI/ADQaDScPXuWtrY2AB49esT9+/dxuVxHate+iXx7e5uRkRFmZmbQarU0NDSc+I4oh4VcLqe+vp7q6mrcbjeDg4MsLS3xuj02Q6EQQ0NDdHR04HK5qKys5Pz5829csclhotVqaW1t5cqVKzidTj777DNGRkZe+718HfZN5MPDwzx9+hSZTMbp06cpKio6tml+xxGVSkVpaSnZ2dm4XC56e3tZWVl5rWvu1e0/f/6c0tJS3nvvPXJzc4Ug6AGTn5/P5cuXyc7OZnZ2Nt4wMhqNHok9+yLynZ0dOjs7GRwcpLCwkCtXrpyonl/HhczMTC5evIhGo+Hhw4cMDw+/8rV8Ph/d3d309fUhl8u5ePEiZ86cORbR3kRHLpdTXFzMpUuXyM7Opru7m4cPH+LxeI7Entd+x6PRaHwkjtvtpqSkhNraWmEv/gqYTCZaW1tJS0tjYGDgewG4vZlgP5W+vj6+/vprYrEYbW1tQiT9kFGpVLS1tdHY2MjKygodHR3Mz88fiS2vLXKn08nIyAgul4v09HSKiopISUkRPMYrIJfLKSgoIDs7m3A4zMLCAsvLy4TD4Z88ZSQajbK1tcXjx48ZGBggPz+ft99++1jmVCc6FoslPmJ5dXWV9vZ2ZmdnD92O11bi4uIifX19SCQS6uvrhSOz10Qmk1FQUEBRUREej4eBgQE8Hk98cOOP4Xa7efbsGWNjY2i1WmpqaigrK0uItlonEZvNxvXr1zGbzXR0dPD48eP4OObD4rVFPj8/T09PD1KplIaGBjIyMvbDrjeagoICqqqq4t10Njc3EYvFP0nk8/PzfPnll6yvr9Pa2nriG2OedJKTk2ltbaWiogKHw0FPTw+zs7MEg8FDs+G1RB4KhVhaWmJ1dRWtVktxcfEbW0a6n2RkZFBRUUEoFGJkZAS73U4sFvvR5fru7i7Dw8MMDAyQnJycEIMdTjpisRir1Ro/cVpZWYmPADs0G171F0OhEIuLi6ytraFSqcjIyDh2JXYnleTkZAoLC0lKSsJut7OysoLX6yUSiSAWi39Q7Lu7u/F54AqFgtLSUvLz84Vg2zGhoqKCs2fPEggEuHv3LlNTU4d271cW+c7ODmNjY2xtbWGz2cjPzxf2ffuEWCyOTwZVKBSsrq6ysrJCMBj8u7kHXq+XBw8eMDo6SkVFBc3Nzfua/y7wepjN5vio7dnZWYaGhnA6nYdydv7KIt/e3mZsbAyPx0NhYSF5eXmC19hHlEolRUVFZGVlsba2xuTkJIFAAKlU+oPPeWVlha6uLtbW1qisrKSmpkZIRjpmZGRkUFVVRVpaGi9evOD58+f4fL4Dv+9riXzv6KywsPDAyiPfVGQyGSUlJdhsNux2O2NjY+zu7iKTyf5G5A6Hg6GhIex2O6mpqZSUlJz4IX2JiFqtprm5merqaiYnJ7lz5w4bGxsHft9XEnksFsPpdMbPcHNycjAajftt2xuNTCaLD1BcX19nenoav9//gxH2vZRirVZLU1MTWVlZR2CxwE+hvLycuro6gsEgAwMDzM3NHfiR2iuJfGdnB4fDQTgcRq/XYzKZhKX6PiMSiTCZTGRkZODz+VheXsbn88ULHb77vIeGhr5XRioEQI8ve9uwnJwcdnd3GR8fZ3l5+UALWF5a5LFYjM3NTdbW1tDpdGRlZQkBngNCLpeTlpaGSqVid3cXj8cTL0Hd8+ibm5tMTU3h8XjIy8ujoqJCCIAec8xmM42NjZhMJgYHB3nx4sWB3u+lRR6JRHA4HGxtbZGSkhKPAAscDBqNBqvVikqlwuVy4Xa7EYvFyGQyAoEAw8PDbGxsYLFYKCgoEPbiJwCdTkdtbS0Wi4WJiQlGR0cJhUIHdr9XFrnT6SQ5ORmr1SpEcQ8QpVJJRkYGOp0Ol8uFy+VCKpWiVCpZX1/n6dOn+P1+amtrKSwsFLZNJwCFQkFxcTE5OTnxldhBdnh9JZFvbGzgdDrRarWYzWYhbfIAUSqVWCwW1Go1brcbj8cTF/Lc3Bz9/f3IZDIaGhqEZhAnBJFIRFpaGjabjeTk5LjQd3Z2DuR+Ly3yaDTKxsYGW1tb8UF+gsgPDpVKhcViQaPR4Ha72d7eJhwO4/F4mJ2dZXl5Gb1eT3V1tbBUP0GIRCKysrIoKysjGo0yPDx8YKmuryTyra0t3G43Go0Gg8EgLNcPEKVSiclkQqVS4fP58Pv9+P1+FhYWsNvtKJVKsrKySE9PF96HE0Z6ejr19fUoFAr6+/tZWFg4kPu8ksg9Hg8+ny8+/0ng4JDJZOj1epRKJTs7OwSDQXw+HzMzM7hcLrKysrDZbELw8wRiMpniwyXHx8dZXV09kPu80p5878OmVCoF73HASKVSdDodCoWCQCBAOBzG6/UyOTmJ2+0mPz+fvLy8ozZT4BVQKBTYbDZ0Oh1OpxO73X4gk1deWuTBYJBwOBw/xhE4WMRiMVqtFrlczu7uLqFQKO7J3W43WVlZZGZmCp14TigpKSlYrVY0Gg0bGxusrKzsa899eAWR7zWLV6vVwhLxkFCr1cjlcgKBALu7u/h8Pubm5vB6vWRlZQkZbicYmUxGdnY2WVlZuFwuJicn9z3K/lIij8VieL1eJBIJWq32RIg8Go3i9/vx+Xzs7u4etTmvhEwmQy6XEw6H2d3dJRAI4Pf7kclk8aCcwMnFZrNRWFjI9vY2o6OjuN3ufb3+S22oQ6EQgUAAiUSCWq0+9vvxvcYWs7OzBAIB0tLSyMvLO5Geb6/H296+fG+Zp9Ppjto0gdckOzub/Px8RkdHmZyc3PfRSi8t8lAohFgsRqFQHNsm/bFYjEAgwOjoKPfv32dkZISdnR2MRiMNDQ2cO3eOzMzMY2v/DyGRSJBIJIRCIWKxGFlZWeTk5Ah56gmAwWAgOzsbv9/P/Pz80Yo8Go0SDocRiUTIZLJjK5JwOMzc3By3b9/m97//PcvLy0QiEeRyOZOTk8jlci5fvozBYDhqU38yEokEsVgcD8qYzWYyMjKERKQEQKFQYDQaEYlEuFwutre39/X6LyXySCQSF7lUKj22EV2/38/w8DAdHR0MDg5+7++6urrIz88nJycHvV5/bL+o/hqxWPw9W00mE1ar9UTERQR+HI1GQ0pKCtvb27jdbgKBwL6t0l5KpXsiB461yHd2dpiammJubg6RSIRYLI6Xw+7s7DA8PMzU1NSBVv7sN98VuUgkinty4RgzMVAoFGRkZKDX69nc3GRra2vfasxfSqV7y3Xg7/YaOw5EIhG2t7fjRxF7ApFIJITDYZxOJx6P58gG0L0Ke/bv/b/ZbMZisZyYlYjAP0Yul5Oeno5er2dra4u1tbV96xjzUiL/7jyuoxzF+mPIZDLS0tJITk4mFosRDofZ2dkhEonEBWIwGE6cQPaevUKhwGAwoNFojtgigf1CJpN9T+R2u/1oRC4Wi5FKpUSjUUKh0LH1hCqViqKiIoqLi+NnyHsrEJPJRE1NDYWFhcf+CPC7RKPR+Juu0WiEmoEEQy6XY7VaSU5OxuVysb6+vm+Zby/1KZdIJPE94HEXeWVlJVeuXMHlcjE6OkogEECv19Pc3Mzly5dP3JzuveNL+LaziHB0lljIZDJSU1PRaDRsb2/jcrn2TV8vLXKpVEosFiMUCh364LafilQqJSsri0uXLiGVSnn69Ckej4ecnBzOnTtHXV3diRvnFA6HCYVCSCQSUlJShKh6giEWi+Nf3js7O3i93qMVOXz7oTuunhy+tTU3NzfeaicQCJCamorNZjuRzRXC4TDhcBiFQoFerxdEnmCIxWKSk5PjIt/e3j46kSsUCqLRKIFA4Nh68j3EYjGZmZkJ0RZp70tVrVYLnjxBUalU3xP5kRyhSaVSkpKSiEaj+Hy+Qx2/+qazV1yj1WoFT56g7DXoDAQC7OzsHI0nF4vFaDQaIpEIHo9HEPkhsbu7i9/vRyKRoNPpBE+ewOzVhOxVHO4HL52yplKpEIlE+P1+QeSHhMfjYWdnJy5yjUZzoo7/BH46MpkMtVqNSCTat7rylxb5Xm2zWCw+sfXZJ4loNBrP3pNIJCQlJZGUlCSIPEHZW7JLJJKj8+R77YiSkpLw+/0H0pNK4C+EQiHcbjderxeRSIRCofjByaYCicFe8ZdIJNq3ZJhXEnlycjJarRafz3dog9TfVILBIJubm7jd7rjI98pOBRKPvToLkUhEJBLZF229ksjT0tLiZXFra2v73nhO4C/s7u6ytrbG1tYW8G1gRliqJy57qePA0YrcaDSi1+vjIhcCcAfHnsg3NjaIxWJxkQuePDERiUT77slf2iVIJBIMBgOpqanxEcaCyA+O3d1dVldXcTgcyGQyZDJZQovc6/UyPz+P3W4Hvp0ykp2d/caMx97z5Ht78v1IOHslkZvNZlJTU5menmZ5eVkQ+QHi9/ux2+1sbGzEh0vufdMnErFYjJ2dHXp7e7l//z5jY2OIRCLKysq4cOECtbW18ePbRGbPk8O3JytH4snFYjEZGRkYDAY2NjaYn58XRH6AbG9vs76+jsfjwWq1xqsAj3M9/6vg9XoZGRnh888/509/+hPr6+sADA4O4vV6kclklJeXCzX0r8BLi1wkEpGcnIzRaCQUCrG2thafyZXo37KHyV7HWYfDQTQajR9bisXiffuGP044HA4ePXrE119/zejoaPzPNzY2SEpKIiMjIz5pJJHZ6xsQi8UQi8X7si175SsYjUZSU1MJBoMsLS3h8/le2xiBvxCNRpmbm2NxcZHU1FQKCwvjPdbD4XDCefK1tTUGBgaYn58H+N4x4fLyMhMTE/EThkRmr5NRLBbbt9jLK18hOTmZ3NxcVCoVs7OzBzZb+U0lHA4zMTHBwsICFouF8vJyUlJS4n32jnsF4Mvi8/lYX19nZ2cHsViMSqVCpVLFB0psbW3t+/ig48h3OwB9t6/f6/DKItdqtZSVlZGcnMzk5CQzMzMJ512Okt3dXSYnJ1lcXMRiscSf9Z7IE225npSURFpaWrzKca9+PhqNolAo4rXWiU4sFvueyI/Uk+t0OioqKkhOTmZsbIypqanXNkbgL2xvbzMxMcHq6ioWi4WSkpK4yPf2bImExWKhqqoKq9UKEB/uCN9uDYuKik7UMIxX5a9Fvh9xrldOnVIqleTm5mIwGHA4HMzNzeFyuU5k15Xjxt4Mt/X1dSQSCVarNd7/y+/3H+vWW6+K2WympaWFmZkZvF4vfr8fkUiEUqmkpaWFhoaGN0Lk322Sul81Cq+VH6nX68nMzCQpKYm1tTWmp6cpLy8Xpmy+JisrK4yMjBCLxSgoKMBisSCTyb5XFJRoqcRqtZqqqio+/PBDjEYji4uLAPG+fBUVFW/E5yoSibC7u0ssFtu3EVivJXKJREJ2djYFBQV4vV76+vqwWq1kZGTsi3FvKrOzs3R3d6NQKDh9+jRmsxmPx4NKpSIWiyVkV569o9mmpibS09NZWVlBJBKRkZFBTk5Owh+d7REKhfD7/USj0X2LQbx2pUNmZiY1NTU8fPiQ3t5eysvLBZG/JtPT04yOjpKfn09lZSWpqan4/X40Gg2xWAy3252wtfw6nY7S0lLy8/PjgzXfpIKcYDBIOByO91PcD147dGexWKivr0cmk9HX18f4+HjCLSUPi2g0yurqKpOTk2xubmKxWCguLkYulyOTydBqtXGRJ3Id/14vQZVK9UYJPBKJEAgEkMlk+/raX1vkGo2GwsJCMjMz8fv9jI6OMjs7m3BHPIeBx+Ohu7ubhYUFrFYrxcXF8UCmQqGIe3KPx5OwnvxNZi/eolar0el0+5ZBui+lTHq9nurqavLy8piamuKbb77B5XLtx6XfKOx2Ox0dHbjdbhobG6msrIz/nVKpRKfTEY1GE96Tv4nstfnaE7lGo9m3SsN9uYpUKqW+vp6WlhbW19e5f/9+PDoq8NOIRCJMT0/T39+PXC7n3Llz5OXlxf9eqVSSnJxMOBxmc3NTEHmCEYlEcLlc7OzskJSUhFarPV4iB8jLy6Ourg61Ws3U1BTDw8O43e79unxCE4vFWFxcZHR0lN3dXXJycigtLY3nqsO3X6R7yTBOp/ONSPF8kwiHw2xtbeHz+VCr1SQnJx8/kcvlcoqKiuJBuI6ODvr6+vbr8gnNzs4ODx484Pnz5+Tm5nL27FnMZvP39mQikQidTodMJiMQCODz+RIu6+1NJhQK4XA48Hg8pKSkYDQa920g5762F9Hr9Vy+fJnKykpevHjBo0eP3ojKodchEokwMzNDR0cHDoeDpqYmzpw584OR1b0lu1KpxOv1CpV/CUQoFGJlZQWXy0VqaioWi+V4ilylUlFdXU1dXR0ikYiRkREGBwfZ3t7ez9skFAsLCzx9+hSHw0F2djY1NTXx/O2/RiqVfq+/nsPhEI4rE4RgMMjq6iput5u0tDQsFsvxOUL7a5KTk6mvr6e5uZnt7W1u3brFxMTEft8mIQiFQnR2dnL//n3S0tJ466234kkgP4RIJMJsNmMymfB4PCwuLiZc5tubSjAY/J4n1+v1x+sI7a8pKCjg7bffxmg08vTpU549eyZ4878iEokwMTHBkydPWFhYoKSkhIsXL5Kamvp3f0csFmMymTAYDHg8HlZWVoTz8gRhZ2eHra0tgsEgKSkp+1pWeyAiVyqVnD59moaGBuRyOR0dHdy9exePx3MQtzuRTE1NcePGDcbHxykpKaGlpQWz2fwPI6oSiQSLxUJaWhoul4ulpSXhKC0BCIVCbG1tEQ6HUavVaLXafW2ldmB9fdVqNW1tbVy4cAG73c4nn3xCb2+vsIcEnE4n9+/f5+uvv0atVvPBBx9w6tSpH/09sViM2WzGbDbjcrlYWFjA7/cfgsUCB8nW1hYLCwuoVCqys7NJSkra1+sfaPPugoICLl++TFZWFmNjY9y8eZP+/v6DvOWxZ3t7m9u3b3P79m1isRiNjY00NjaSkpLyk34/JSUFi8WCz+djcXERr9d7wBYLHDRLS0vMzs7GU8S1Wu2+Xv9As/9VKhXl5eW89dZbeL1enj59ikqliveHe5OKD+BbgT9+/JhPPvmE1dVVLl++zJUrVzAajT/5GnK5HIPBgEqlivdFC4VC8VbNAiePmZkZxsfHSU5Opqys7HtJUPvBgY/h0Gg0XL58matXryIWi7l//z5ffvklc3NzB33rY8ezZ8/45JNPmJycpKCggGvXrlFaWvrS19FqteTk5JCUlMTi4iIOh+MArBU4DPa68k5PT6PT6SgpKdn32vlDmbVjNpu5fPky169fRywWc/PmTb766qv4KJxEZ3d3l+fPn/PHP/6Rvr4+iouL+eCDD6ipqXml/ZdaraawsBC9Xs/8/DyLi4tC9tsJxeVyYbfb8fl8pKWlYbVa932Fe2gDtXJzc/nnf/5nLl++jM/n4+7du9y7d4+VlZXDMuFIiEajDA4OcuPGDQYGBsjJyeGf/umfuHr16ivvvZKSkigsLCQlJYW5uTnm5uYSrufbm8Du7i6zs7N4PB70ej0Wi+VAOtIemsilUil5eXm8//77XL16FafTye9//3s+//xzFhYWDsuMQyUcDtPZ2cnvfvc7Hj58iMlk4pe//CXnz59/reBKUlJSvHvr5OQkExMTwqnFCWRzc5ORkRH8fj/5+fl/N9PxdTn0yNepU6dQKpWEQiEePnzIrVu3EIlEXLlyhaysrIQJIO31vLtx4wbPnj3DYDDws5/9jHfeeee1o6cymYyMjAxMJlM8yr62tkZmZua+5TsLHDxLS0t0d3cTCoU4c+YMmZmZB3KfI5l/W1hYyL/8y7/w7rvv4vP5+Pjjj/l//+//JUz6azAY5OHDh/znf/4n33zzDenp6fzqV796rSX6X6NQKMjOziYzMxO3283Q0BBOp3Nfri1wOCwsLDAwMEAsFuPUqVOkp6cfyH2O5AxLLBZTUVGBUqlEIpFw584d7t+/j9fr5fr16/GhDSeR+fl5Ojs7+eyzz5iYmMBms/HBBx/wzjvv7PvRyF4Nf39/P48ePYpPmxU43ux1gVlYWMDlcsUbV+53Eswekt/85je/OZAr/wT2zsvlcjnz8/MMDAzgcDjQ6XSkp6efqKV7LBZjaWmJL7/8kv/7v/9jamqKU6dO8atf/YpLly795GSXl0EulxMOhxkeHmZubo78/HzKysr2/T4C+0sgEGBoaIinT5/i9XppbGzk7NmzB/Z5P9JsFIlEQmZmJm+//TZJSUncvXuXmZkZ/uu//ovJyUna2tqoqqo6ShN/Ei6Xi2fPntHe3k5vby/RaJSLFy9y/fp1Wlpa9j2DaQ+dTkdVVRUGg4HR0VEmJyfZ2tra1womgf1nZ2eH58+fMz8/T0FBAeXl5Qc65+1IPfkeOp2OoqIirFYrfr+f4eFhpqenCYfDiMViZDJZ/L/HhUgkEi/3fPbsGbdv36azsxO1Ws3Pf/5zfvnLX1JXV3egUz9EIhEqlYqZmRlmZ2eRSqVYLBbMZvOxelYC32d+fp4bN26wurrKuXPnaGpq+ofVh6/Lsckr3atcU6lUmM1ment7efLkSXxgQ2trK42Njcdmksb8/Dzt7e10dXWxsrKCSqWitbWVuro6GhoasNlsh2KHXC6nqqqKsbExFhYWePz4MQUFBW/ESKGTyPb2NuPj48zMzKBQKCgrKzuwgNsex0bk8K3Qa2trycvLIz8/n/v37zM0NER3dzdOp5O5uTny8vKwWq1YrdZDDc7FYjFWV1dZXV1laWmJ8fFxBgcHsdvt6PV6mpubuXz5MuXl5Ydm0x4lJSU0NTUxOTlJd3c358+fx2q1Ckv2Y8jExASdnZ2IxWKqqqrIz88/8JHMx0rke6SkpNDS0kJ+fj5jY2MMDAzQ399Pb28vBoOB6upqmpubqa6uPpRocigUYm5ujqdPn/LkyRMmJycRiUTk5ubyT//0T5SXl2Oz2bBYLAduyw9hMpk4deoURqORlZUVxsfHKSoqIi0t7UjsEfhhgsEgXV1dDAwMkJeXx4ULF16qOOlVOZYih28j78nJyRQUFJCVlYVer2dkZASXy8XExAR2u50HDx6QlpaG0WgkPT0dk8kUb53zKscReyOIXC4Xm5ub2O12VlZWcDgcrK+vs7W1hdfrxWg0YrPZ4m2uDipT6acilUrJzs6mrq6Ohw8f0tfXR15eHmfPnj1SuwT+QiQSYWlpKZ7PcO3aNerq6g7s2Oy7HFuR7yGRSKiqqqKwsBCn08n4+Djd3d309vby7NkzANLT08nPzyc7Oxur1YrZbMZoNJKcnIxCoUAkEsV/vkssFosPfff5fDidTtbX11lfX2d5eZm5ubn4XDKlUkl5eTlXrlzh9OnT2Gw2tFrtsdn7ajQaWltbWV9fZ3BwkGfPnlFdXb3vZ/MCr4bD4aCzs5P19XVyc3OprKzEaDQeypbq2IscvvVUWq2W/9/enT41dYYNGL/IwhaYyBIIaA2yDJthLUshtggo48AM/dA/sR+cdqbTaqUoBWkBKSgIbVk0Ao1hJ0AgEOBk4f3QyRn7vq1vFyVwcv9mMvrx6HBxlpznuVNTU0lPTyczM5OCggJev37N7u4uR0dHKIrCixcvmJmZIRgMEggE0Ol06rDAyJ96vV4NW1EUTk5OCAQChEIhdYpmZJJmUlIStbW1mEwmMjMzyc/Pp6SkhPz8/HN3v2s0GikrK+Ply5eMjo7y66+/sri4SHl5uTxpPwfm5+d59OgR4XCYlpYWSktLz+xn6EJE/qaUlBSqq6uprq4Gft86Z2lpiYWFBVwuF2tra+rldWQAQSRag8Hwh8gDgQCBQIBwOIzRaCQtLU3dDTU3NxebzUZhYSGXL1/GZDJF+V/+dpHhC+Xl5Vy/fp3l5WUGBgbUZakiOsLhMF6vl4mJCV69ekVtbS03b94kOzv7zI7hwkX+v6Wnp5OcnMyVK1fY39/H7/ern+PjY/UsHQqFCAaDhMNh4uLi0Ol06PV69Ho9RqORhIQEEhMTSU5OJjk5WZ0saTabL9Sij8LCQu7cucPdu3fp7+/HarVK5FHk9XoZGhpibm6O7OxsqqurycvLO9OfqQsfOfz+1VtiYuJbfzuenp6iKIp6WW4wGDR5GWs2m2lqauKXX36hp6eHZ8+eUVVVRUFBwTsbai/+PpfLxXfffcf6+jq3bt2ioaGB+Pj4Mz2GqKxCi4a4uDgSEhLU4fZaDDwilElPdAAACS5JREFUIyODhoYGqqurcbvd9Pb2srKyEu3Dijkej4fJyUlevnxJeno6N27coLCw8MyPI2YijzUVFRW0tbURCAQYGBhgdnaWQCAQ7cOKGaFQiB9//JHBwUEuXbrExx9/TFFRUVROLhK5RlksFurr6ykvL8fv9zM8PMz09LRsE3UGFEVhbm6O/v5+VlZW+Oijj2htbY3aK9mauCcXf85qtdLZ2Ynf7+fZs2fEx8djtVrf2w4k4ncLCwv09vaqr2E3NjZis9ne2bzxf0rO5Bqm0+n48MMPuXXrFmazmYmJCfr7+2Nml9xo8Hq9jIyM8MMPP5Cenk5nZyelpaVRnTEgkWtcfHw8lZWV3LlzB5PJRG9vL0NDQ4TD4Wgfmubs7e0xPj7O2NgYgUCAuro6Wlpa3usy0r9DIo8BOTk5tLe3U1NTw8bGBo8fP2Z8fFzmqL1js7OzfPXVV7jdbhwOB62traSlpUXtMj1C7sljgE6nIy8vD4fDgcfjwel0cu/ePXQ6HdXV1Zr+OvEshMNhnE4nAwMDvHjxgtLSUrq7u6Oy7PjPSOQxxG63EwwG+fzzzxkfH1dfIrLb7efuXfyLxO128+WXXzI0NERBQQGdnZ0UFxefm/9TiTyGmM1mGhsbWV9f5/79+/z0008Eg0EURVF3zxX/zPz8PA8ePGBwcBCz2UxXVxeffPLJmb/V9jYSeYxJTEykvb0dnU7H3bt3GR0dxWw2YzKZ/tXwxVi2vb1NX18fDx8+xGw2093dfa62KIuIO5VJeTHJ4/HQ09PDb7/9RlZWFnq9nnA4THp6OjU1NRQUFET7EM8lj8fDyMgIq6urpKamsr6+jtfrpaysjNbW1qjtDvQ2EnkM8/v9BAIB1tbW+Prrr3n8+DFJSUl0dHRw+/ZtLl++rG66EctOT08JBoPs7e0xNDTEF198wfr6Os3NzbS3t2O329U1EefRudiSWUSH0WgkMTERs9mMTqcjFAqxtrbG4uIiHo+H+Ph4LBZLzD99VxSFhYUFvv32W3p6evD5fFRUVOBwOKitrSUjI+Nc/x/JPbnAaDRy48YNLBYLW1tbPHjwgM3NTXJzc6mrq4v24UWd0Whka2uLhw8fMjY2RltbG59++in19fXn6gHbX5GXYYQqPj4eg8HA6empumuOLGhB3UVIURTC4TAGg4GEhIRzffZ+k5zJhSohIYH6+noODg5YXl7m6dOnpKam0tjYGLMP4lZXV3n69CnDw8PodDra29tpamrCbDYTCAQuxJlcHrwJVTAY5OjoiOfPn3Pv3j3167WOjg66urq4evXqhTl7/VfBYJCVlRUGBwe5f/8+LpcLu93OZ599Rm1tLWlpaRiNxgvxUFIiF//H0dERExMT9PX1MTU1hd/vx26309HRgcPhOPebWv5XJycnjIyM0NfXx/T0NIqiUF5ezu3bt3E4HBdurLZELv7S69evGRgY4JtvvmFzc5PKykra2tqorKwkKytLc3u6HxwcqPvWP3r0iKmpKUwmE62trXR3d1/Yl4UkcvFWq6urTE1NMTQ0xPT0NMFgkMrKSlpaWt77NM6zdHBwwNjYGL29vUxOThIIBLDb7TQ3N1NXV0dBQUHUV5P9WxK5+Fumpqbo6elhbGyMUChEdnY2ZWVllJeXU1xczNWrVy/U1tURy8vLOJ1OZmZmmJ2dxel0AlBVVUVXVxcNDQ0X/p1+iVz8LYqi4PF4mJubY3R0lKGhITweD3l5edy8eZPm5maKiopISko697GHw2EURcHtdvPkyRP6+vpwOp2YzWZqampoamri+vXrWK3WM5lV9r5J5OIfCYfD/Pzzzzx58oTnz5+zvr5OOBwmLS0Nm81GWVkZpaWllJSUnLtAFEXh1atXTE9P43Q6cbvdeL1eTk5OyMzMpKKigsbGRqqqqi782ftNErn4xyIvyywuLjI8PMz333+vXuYWFRVRUVFBRUUF165dU4dCRj5ndZYPhUIcHx9zdHTE8fExe3t7uFwu5ubmmJycxOl0EgwGKS0txeFw0NzcTH5+PsnJyRf23vuvSOTiP3G73czPz+NyuXC73WxsbLC9vY3f7ycpKQmr1UpxcTGFhYUUFhaSl5f33r9rVxQFl8vF4uIiTqeTxcVFlpaW8Pl8mEwmsrKyyMrK4sqVKxQVFVFYWIjNZrsQ33n/GxK5eGeWl5eZmJhgcnKSmZkZdnZ21G2gLRYLmZmZWCwWLl26REpKyh/mzkWm2hgMBnQ63R8+gDqkMhwOq59AIMDR0RGHh4ccHh5ycHCA3+9nd3cXj8fD1tYWm5ubeDwe9vf3SU1NpaSkhObmZqqqqrh27Zrmztp/RiIX79Tu7i67u7vs7OywsbHB2toaq6urrKyssLy8jMfjUdetWywWrFYrWVlZZGZmkpKSQmJiIjqdTg1er9cTFxenPiwLBoPqu+SHh4dsb2+zvr7OxsYGq6ureL1e4uLiyMjIICcnh5ycHHJzc8nNzSU7O5uMjAwyMjLOxQaLZ0UiF+/VxsYGS0tLLC0tsbi4yMrKCj6fTx06GRk8qdfr1egiZ+zT01N162idTqdOo438/c0R1MFgkJOTE3WEc05ODjabjby8PGw2Gx988IFmL8f/PxK5eO8iEUZWth0eHrKzs8P29jZbW1tsb2+zu7uLz+fD7/ejKIr6wOzk5AT4fYVcZOPJyJjplJQU0tLS1NsAi8VCeno6JpNJXVEXuSKI1cBBIhdR5PP52N/fZ39/H5/Pp0b95i+EyJDGSLCRj8FgICkpiZSUFHWO/EV7p/ysSORCaFxsPHkQIoZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJonEQuhMZJ5EJo3P8A6nkt8Mu0OswAAAAASUVORK5CYII=)
maths-General
maths-
In the diagram AB is tangent and ACD is secant, AB = 6 cm and AC = 4 cm, AD=
![](data:image/png;base64,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)
In the diagram AB is tangent and ACD is secant, AB = 6 cm and AC = 4 cm, AD=
![](data:image/png;base64,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)
maths-General
maths-
The two Circles below are concentric, the radius of the larger Circle is 10 cm and that of the smaller Circle is 6cm. What is the length of the chord AB ?
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)
The two Circles below are concentric, the radius of the larger Circle is 10 cm and that of the smaller Circle is 6cm. What is the length of the chord AB ?
![](data:image/png;base64,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)
maths-General
maths-
Given O is center of smaller Circle, BD is common chord, ABC, EDO are straight lines. If AED =130°, then C O D =
![](data:image/png;base64,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)
Given O is center of smaller Circle, BD is common chord, ABC, EDO are straight lines. If AED =130°, then C O D =
![](data:image/png;base64,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)
maths-General