Maths-
General
Easy
Question
If
do not differ by a multiple of
and if
Then k equals
![plus-or-minus 2](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABYAAAANCAYAAACtpZ5jAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIFJREFUeNpjYCAPWAPxGiD+BMS/gPgCEEczUAEcBOJIIOaB8rWA+ChUjOpAHogvEVL0n0zDf9DCYEtocFDVYA4gPgmNVKyG4cL4gCAQbwBiN2JcQKyLlaCGqhDrNWIM1gDi2UDMRUqYETJYHIhXATELtdPsFqiLiXYlsZFHbkRTDgCK2Smw7tNS7AAAAFh0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4QjE7PC9tbz48bW4+MjwvbW4+PC9tYXRoPipXgugAAAAASUVORK5CYII=)
![plus-or-minus 1 half](data:image/png;base64,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)
- 0
![plus-or-minus 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABYAAAANCAYAAACtpZ5jAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAADVJREFUeNpjYKAMqAFxLRBfYKAyWAzEaUD8n4FG4D/VFQ5Pg//jwaNhzEAr9QMXeeRENGUAAPfZJVq5S7u7AAAAWHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4mI3hCMTs8L21vPjxtbj4xPC9tbj48L21hdGg+l53uJgAAAABJRU5ErkJggg==)
The correct answer is: ![plus-or-minus 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABYAAAANCAYAAACtpZ5jAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAADVJREFUeNpjYKAMqAFxLRBfYKAyWAzEaUD8n4FG4D/VFQ5Pg//jwaNhzEAr9QMXeeRENGUAAPfZJVq5S7u7AAAAWHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4mI3hCMTs8L21vPjxtbj4xPC9tbj48L21hdGg+l53uJgAAAABJRU5ErkJggg==)
Related Questions to study
maths-
From the figure AOC=
![](data:image/png;base64,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)
From the figure AOC=
![](data:image/png;base64,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)
maths-General
maths-
In
ABC, D,E,F are the midpoints of sides BC, CA and AB respectively then ar ![open parentheses B D E F close parentheses equals](data:image/png;base64,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)
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)
In
ABC, D,E,F are the midpoints of sides BC, CA and AB respectively then ar ![open parentheses B D E F close parentheses equals](data:image/png;base64,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)
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)
maths-General
biology
When the solute has been added in the solution, then following observation can be made ?
When the solute has been added in the solution, then following observation can be made ?
biologyGeneral
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
![t h e n space a l l space p o s s i b l e space v a l u e s space o f space P space i s](data:image/png;base64,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)
In
![t h e n space a l l space p o s s i b l e space v a l u e s space o f space P space i s](data:image/png;base64,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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,iVBORw0KGgoAAAANSUhEUgAAAOQAAADaCAYAAAC2J+5QAAAgAElEQVR4nOy913tbV5qn+yKDSEwgwAwQYBRFUiIlK1myUnVX90yVXXI/Pc8856Kf/pPOxcxd3820q8pBrp5Tru6eKpdtWYmSmMQcEUgkksgZ2NjnQgWUJCcFkgBJvDcO3AAWNvZvrW996wsSURRFqlSpUhFIyz2AKlWq/JWqIKtUqSCqgqxSpYKoCrJKlQqiKsgqVSqIqiCrVKkgqoKsUqWCqAqySpUKoirIKlUqiKogq1SpIKqCrFKlgqgKskqVCqIqyCpVKoiqIKtUqSCqgqxSpYKoCrJKlQqiKsgqVSqIqiCrVKkgqoKsUqWCqAqySpUKoirIKlUqiKogq1SpIKqCrFKlgqgKskqVCqIqyCpVKoiqIKtUqSCqgqxSpYKoCrJKlQqiKsgqVSqIqiCrVKkgqoKsUqWCqAqySpUKoirIKlUqCHm5B1ARiAUKQp4CUpDKkSJAQUAoSBClcuRyydGduUSBgiBQQAZS2V++e568IFIQAYkEiUSGVCpFJpUglQJIyjzoo0tVkABCjnwiTDyVJSFIEQsFJGKBAnJkah0afS21NSAr9zj3AyGLkIgQTeVJ5qUg5pGIwl8FCSCRIpEpkStr0GlrMGhVyKRVUe4HVUECIEEipok5p1hc3sCR0CM2dNLWoKVJK1DI50hkVCgNJtpsnXQYVajKPeQ9Q4KYTxFZn2RxxY0jZUBW10qbsYYGrZxCNoEQ97MdLbAtsWK19/LukAm9uirI/aAqSACZAnmNjNTmFIv//v/xZaIf+ekPuDkIhoyH7U0HTxcjRJRd2K/c4PK7A/TXSlCXe9x7gUyFTCUh5XjIwr9/yf9Nj6AZ/jl/f1qJUa9AyKfIhRbZXAvzKFYgVGhjrK+AXn1kjfiyUhUkPNsnqQpk4yFCrm2iuhFMzTaau7R0qDToNGoI3WFm7RHjf1YRKahQXelgoFZZ7pG/PRIJMhVkoztEPF6i+vPoTd20WAy0m5WIGT3Zum0y8l2CHjNGrQ6ZpCrG/aIqSAAyUNglloQ4Nlp7TjN2aYiRXhldim6sYoZT5hRNv/+C//ePd/k6ocfeVUeroRGD5LC7OPJQCBNNysjIbHQNnuHs1VOc6oc2GYhCA2K7igZLmjavCaXaiFZVFeR+Ub2zAMQh7GR7N4Un34HW1EGfRU6TUoJEIkUqrUHW3UV7l5HGuIvo/FMW3FGceSiUe+hvTZhCzIFvO4c31UF9Swf9fWCUAUKGRDRFtmCkztjLQE8TtnYZyuo0vm9Uby1ALozgXsa3G2erxsZpo4kuHS/uEZX1KJuMNMkTKCNbeLeT+DIwoDjk3td8kNzWMlv+IGvxOnriQbLuRVbzGWLbScLZWixd7fRZVKiOxKa5sqkKEiASIby2QSCeJdlmpaG5mXYJKF66TAJIJAXEQh4hX0AQyjHYPSYSJra+znYkwraqgeaQl8DDANGgm9WQibTpGjealAyUe5zHhKrJCmQiQTZXXASTBXSWLkzNTehfvkhIUUikiGfl5JQ6tAYlOuXhv4GZ4A5bK05Cohr94Bjd/f3YFCLaoJtEOExEriWrfHlqqrJfVFdIBKLhbVY2osQz9bRbW2lu1r7kqBFh10fE7cOf1yOYumhr0WJWH3ZBCkR2/Kysh0kpT9Bz6QYXr9u5gJbtXJhkrIXtvkbqGw61UX6oOOaCFAAv0ZCPVaechNqErauOZvPL12VIbKyyvrSBX92FrneYfnMtrYfawyoAPkI7ftYccnKNrdhPdGK1KqlJ2WjtSTCUNxC0aGk2lHusx4djLkgRchvEdvw4kmbyzd30WWux1Dx/TYJ8YIapBwvc31Cg6B5m5MpJ+hs16Mo17D0hD/l1wru7bCRakNo66WtX0CgDlHXILUNYJArMBgWaqsV6YBxvQRaSsLnGttuDS1qPqrGNdr2UxuevCS7jmfqSu3NxlqXvMHTxIv/1cgsdhkNuxglx2Foh4N3GITVhNLZiqfvLd1eoob4Jg0SCTio9xFbA4eP4ClKIE/PMs/X1V3x75zHT/hO0hfx4ZieYr5WRTifJZXKkQxv43SlizWcZPnOOy5dPcqZJgbbc438b8nFim7NsffUVd+7OMB08zXBeQiGZQVorf2aHy2TP/lHusR4zjq0gRSFFcncLx2YEX1yK3iBFLw2zvbbEoqZAPBImGU8Sy2uQ1Z1l6GeDjAx20lmrpOan376CESGfJLnjZcMVIZCQoG9QY9BKySVyZEVQVZfEt6BAIZ9HKEABGTK5DPlznj9RBMmP3F+JKIriD//56CLm48R862wuz7PsjhKQGNE3NtHRoEAtF8mkkuQyWdKSWlQNVrq6W7EeCeeGCLk4Ue8a7uUFFjcT7CjbMVt7GOp5luVRTeR4U0SI+wh4fPijeVKKRmqbzHQ0KdAoRFJZOSIyahQ/LMpjK8gqVfYGEfJhIjsRdsMR4tEosWiMWCpPTl6DQqFCI+ZRGRpQtNsxG/W0KOGH0kmPrclapcqekA8QX3/M+INlZrYkSIwddNg6aW2RYCi4cc8+4E9fewnVDzL4/xi53Kyn+UcskKogq1R5I/KQ8bA1dZ8Hdx4z5YV00yBdxhaaO7qwNsmoy0Peu0YuEiGY3SEr5JDKfvzsuirIlxBFkXw+Ty6X47hY8xKJBIlEgiiKxONxBEFArVajVCpL//84UrwvxX+XyWTI5fJn/y8bIL3yJ779wx0+fyxHc+Yaf/tff8aZ9hrMmhpUcpCLJ+g8JefC3+ix5WuwN6lpoCrIVyaTybCxscGDBw+Yn58nk8mgUDw7FZf8mGvskFIUmkQiQaVSIZPJSKVSZLNZZDIZMpkMURRfuO44IIriCxORVCpFoVBw4cIlrt94D02NlkRggbk//gd3H+3g0v6Cq0MXOD9opPOFW6ShtrWPwctSujICjUYttVQF+coEAgG+/vprbt++zfz8PCqVCoPBcKRXiOKMH4vF2N7eJhKJkM/nUavVGI1G6uvrUSqVCEciteXVkclkpNNpgsEgkUgElboGJEouXz4LqjQ7i4/58x9XWIz20PFf3uPsmPUlMT5DIlNitFgRCyIajeY7GUQvUxXkc6yvr/Pw4UOSySQXLlygr6+PpqYmCoUChcLhT0V+GYlEQk1NDZlMhgcPHvAf//Ef5HK50t9GRka4dOkS9fX1pFKpIz0xPU/xvgQCAR48eMDMzAxarZ7aBiNKSQFii/gX5njilBNq7+biSDs9bd//XlKpDJ1e/5fUvZ+2MKqC/Av5fJ7FxUUWFhaw2Wz88z//M4ODg9TX1x9JQUqlUtRqNZFIhMnJSdxuN21tbQSDQQCam5u5cuUK//RP/4TRaCSZTJZ5xAeHRCJBo9Gwvr5OPB4nFosxPHKK8xfPo1ZIERxzeNY3cRaakbX20tdeQ+sPLH2vKsQiVUH+BZ/Px/r6OolEApvNxtmzZ6mtrS33sPadtbU1/v3f/53l5WWampro6upia2uLXC6HIAjo9XqkUik63eEOpX8TCoUCW1tb5PN5Tp8+xcjwCSTSBBmPl+1QnERNByajCXONjL16UqqCBGKxGHNzc/j9flpaWujt7T3yYhQEgYcPH3L79m0mJiYwm82cO3eORCLBnTt32NjYwO/3k06nqak53MGCb0IikWBjY4Pt7W10Ov2zZ0JTA7kE+WicdDZPTq1BqdOgl0n3LC+2KkierY4PHjwgFosxNjZGX19fuYe0r2QyGaanp/n444+ZnZ2lo6OD3t5ezGYzUqmUra0tPB4P4XCY3d1d6urqjo2HtYjT6WRqagq5XE5PTw/NzS3P/iCRIdPVoNGqUObTCMkUaeEH7o1YQBQEClIZSJ+J9qfuYlWQgNfr5dGjR+TzecbGxujt7S33kPaVBw8ecPv2baamphgcHOTmzZt4vV7+z//5P2SzWUKhEFqtFqVSidfrxWw2o9d/p6jJkWZxcZGpqSnq6uoYHR2lsfEvSXkyJaqOdswtDTSO75L2ethMiETgu2ZrIkYqESdVY0Cm06OT/rTgDncFirdEFEWSySQulwufz4dOp6Ovr4+6urpyD21fSCQSL5ipFouFDz74gBs3bhCLxfjd737HH/7wB7a3t2ltbUWn0+F2u9nd3S330A+UZDLJ/Pw86+vrtLW1MTY2hlb7l4Q7iRJ5+wj2kdNc7MxTuzvB+DcP+WrRjWs7RDAUJLTtI+DZwuH249lNEs8UKACv4qM+1itkPp9ndXWV1dVVdDrdX0yT5nIPa9+YmJjgk08+YXJyEpvNxq9+9SvOnz+PXq8nnU6jVCqpq6vjzJkzdHR0IJFIcDqd9PT0YLVayz38A0EURdxuNw6Hg0wmg8ViwW63o1QU3ahy0A5hGU3xC38U2YNN5v787/xpd4T0KSsWA8jTURIpkZS8Hn1TO52KGnSSVxPbsRZkNptlcnKSpaUlLBYLo6OjR9KbmE6nmZiY4NNPP2VycpLOzk5+9atfceXKlZIparfb+eUvf4nJZOLcuXPIZDKmpqZwOBwEAoEyf4ODIxgMMjs7Szgcpr29HavVilr9fEFaCUh0aDpOcfpnGYSGRRodkFMKFJJxYnI1GqkKhU6BUluPobEWQ40S5StuwY+1IKPRKDMzM3i9Xm7evMnJkydLoXJHhWw2y9TUFL/97W+ZnJykq6uL999/n5/97GdoNBrgmaXQ1NTEhQsX6OrqYnh4mGg0yvT0NC6Xi+3t7TJ/i4PD6XTy8OFDRFHk3LlzWCyW779Q3oDafo132t5hKBolHEkQT4Og0KOp01NfW4NGIUcmk7+QoPxTHFtBFs+YVldXyWQy9PX1YbFYkMmOTtEKURS5d+8en3/+eWnP+Ktf/YpLly6VxJhOp1lZWeHhw4d4PJ7SfUgmkyiVSnw+H9vb26X4zqOOw+Hg8ePHNDQ0cO7cOTo7O3/4YqkapUaNUtNIrTFBMp4jI1Gh0NSge8N5/dgKcmdnh4WFBVKpFG1tbVit1tJDehRIJBLMzs5y+/ZtJicnsVqtfPDBB9y8efMFs3x3d5dvvvmG27dvE4/HOXfuHHK5HIPBQG1tLRKJhEgkQiQSKf33UaRQKJBOp3E6nezs7NDd3U1/fz8GwyuWiZBr0dTB2z5Bx9bLurKywtOnT9HpdJw+fRqTyVTuIe0pExMTfPTRRyUxFveML++RA4EADx8+ZH5+nnA4/MLfjEYjJpOJVCqF2+0mk8kc5Fc4UNLpNPPz87jdburr6+nu7qapqenAx3FsBTk7O8vExARGo5F3332XhoaGcg9pT0gmk9y7d49PP/20ZKbeunWLa9euYTQav3N9MBhkZWWFbDaLWq1+wYFhNpuxWq1ks9lSWOFRJZFI8ODBA1wuF/39/QwPD6NSHXyf7GMpyFAoxNraGj6fD7PZzODg4JHwrgqCwPT0NL/5zW+YmJigq6uLW7ducfPmzR88W5XJZCXzdGho6IVVwWQy0dHRQSaTwel0Eo1GD+qrHDi7u7tMTU0RCoUYHBykr6+vLOb5sdtDxuNxlpeXCQQCGAwGLBbL964chw1BEPj2229Le8bOzk4++OADLl++/KOTjdls5ubNm4yMjHD69OkXopTMZjMdHR0sLy+zsbFxZAWZy+Vwu92sra0hk8kYHBykpaWlLGM5doLc3t7m/v37xONxTp06dSTC5JLJJDMzM3z22WelQ//333+fv/mbv/lrhMn3kM/nSafTNDY2YrfbOXfu3AsPYkNDw7FYIX0+H4uLiwiCQFdXFxaL5aWzx4Pj2JmsHo+HR48ekc1mGR0dxWazlXtIb82jR4/49a9/zfT0dMmB8+677/6oGAuFAn6/n7t37/Jv//ZvjI+PE41GkUr/+kjU1NTQ2tqKKIr4fL7vOH2OAvl8noWFBZaWlmhqamJkZIT6+vqyjedYCTKbzeJwOFhbW6OmpoZTp06VxZO2VxQdEZ9//vkLETjXrl37ye9VdNT8+c9/5osvvmBycpJoNEo+ny9dI5VKqaurw2AwUCgUCIVCR65yQCaTYWJigoWFBaxWK+fPny/r8dexEaQgCGxtbbG+vk6hUKCjo4Ourq6yeNL2iqmpKT766CMmJiaw2WzcunWL69evv9LZWTabJRAIsLOzg1QqxWQyYTabvxMYoVKpaG9vp7Gxkd3dXbxe75GqnrCzs8Py8jI7OztYLBYGBwfLZq7CMdpDptNpZmdncblctLa2MjAw8OqHvhVGLpfjwYMHfPrpp0xNTdHR0cEHH3zAu++++8qJ1VKpFK1WW4rK6evro7Gx8TueRblcTkdHBw6Hg93dXdxuN62trUcioikSibCyskIwGKShoQGLxVJ2b/uxEWQ4HGZ8fByPx8Po6ChDQ0Mv7JcOC6lUiunpaT755BOmpqaw2Wz88pe/fCE29VWQSCSo1Wq6u7sxGo2cPHnye1eGoiBNJhO7u7u4XC5Onz5d1lVkr3C73YyPjyOVShkbG/vhuNUD5PA9kW9IIBBgZmaGcDjMiRMn6OvrO5SCfPjwIR999BFTU1OlcLh33333tfc9iUSCtbU1EokEAwMD9Pb2Ipd/d35WKBS0t7e/IMijErGzsbHBo0ePUCgUnDlzhra2Hygdd4AcvifyDUgkEjgcDsLhMLW1tXR1dR26uMx4PF7K9J+cnCwlF1+/fv2NHFOBQIBHjx4xOztLoVBAp9N97/2QyWQ0NzcfOUGm02nW1tZwOp3U19dz6tSpikhMP/Ima6FQYHl5mbm5OfR6PSdPnsRsNpd7WK/N5OQkH3/8cclMfTmf8XUQBIHNzU3m5ubwer0EAgEymcwPZnQYDAaMRiPpdJpAIEA8Ht+Lr1Q2crkcGxsbuFwuZDIZFouFrq6uiki9O/KCBJiZmWFychKz2cz58+f/Wh/lEJBOp3ny5Elpz1hMobpy5cobn5dFo1FWV1dZX18nnU4jk8l+dE8ok8lKxx+5XI6dnR0ymcyh9VBHo1Gmpqbw+/1YrVZ6e3sr5rsceZM1FouxtLSE0+mktbWVoaGhHz0wrySKycW/+c1vShE4H374IT/72c/e6vA6nU4D0NTURH9/P/39/RiNxh814XU6HVarFa1Wy+bmJqFQ6I0/v9wUzfVYLMbo6Cg9PT3lHlKJI71CFkO+Njc3AbBarbS3tx8Kl70oity9e5fPP/+85MB5Obn4TTEYDJw+fZr//t//OxqNhqGhoZ+svVoUZCaTYWtrC7/ff2jrD3k8Hqanp5HL5Zw6dYqurq5yD6nEkV4hd3d3mZiYIB6PY7fbD00gwMsROMU9482bN986EF4URXZ2dohEIjQ1NdHX1/dKuaAvr5A+n++txlEORFEkFovhcDiIRqM0NDRgt9srqsTlkRbk5uYmExMTAIyOjtLe3l7mEb0aT548KR1tdHV1lfaMe2Fq53I5vvrqK/7H//gffPzxx6yurr4QLvdDFIMItFotW1tb+Hy+QxdCl8vlmJubY2VlBaPRyODgYMXlwR5pQa6trTE1NYVarebChQsVb2I9n1xcPNq4desWV69e3TNHVCaTYWpqii+++IIHDx7g8/nIZrM/+Tq1Wl0qc1JcIQ9bCF0mkylVRyhmt5Q7Mudljqwgg8EgGxsbBIPBkmlWSabJy+Tz+RccON3d3aXk4r3sM5LL5UilUqXzxZaWFpRK5U++TiqV0tTUhMFgIB6Ps7u7e+gqCEQiEebm5vD5fNhsNgYHBytuC3MkBZlMJllcXGRrawuj0YjNZvtJL2I5EQSBu3fvlsRYTC7+qRSqN+H5rlZ9fX309PS8cjMdmUxGQ0MDBoOBVCpFIBAo9ZOsdFKpFA6HA6/Xi0KhwG63YzabK+6ZOJKCDAaD3L17F5/Px6lTpxgeHq7YMLlEIsGjR49KZurzRxv7UcmgWIP1zJkzXLp0iZ6enteKSzUajVgsFgRBwOFwHJpV0uv1MjU1RaFQoK+vj87Ozor0tlfmU/qW7Ozs8OTJE4LBIMPDwwwMDFTcTFjk0aNHfPTRR0xPT5ccOJcvX96XnLx0Ok0ikaCrq4uf//znXL58mebm5tearBobG+ns7CwJMhKJ7Pk494OiP0Gj0TA2Nlax0VpHTpCpVAqXy8Xm5iYqlYr+/v6KvPmJRIJ79+6Vym5YrdZSPuN+1fjxer3cu3ePxcVFUqkUer3+tfdQL6+QhyFAoFgVYH5+nqamJs6fP18Rcavfx5ESZKFQwOVysbS0VNontLW1VeTqODU1VSq7YbfbS5n+++l42tjY4LPPPuN//a//xR/+8Ac8Hs9rv0cxb7BQKBwaQfp8vtLZY2trK319fRXbhPZIReoUCgXm5+eZn5/HbDZz+vTpstZH+T5yuRz379/ns88+Y3p6+oXy/vudMO3xeLh37x67u7uoVCqSyeRrv4dOp6Ozs5NCoYDT6ax4QRY9q9vb27S0tGC1WivuqON5jpQgE4kEMzMzOBwOLly4UHGJtMXk4o8//piZmRnsdjvvv/8+N2/ePJA6Lmq1ulRVbmxs7I3SthQKBSaTCbVaTTweJxQKIQhCRTpI4K9meiKR4J133qn47thHSpB+v5+VlRWi0Sg2m43e3t6KSKkpUgyHm5mZKSUXX7x48cCKKhULJ8diMYaHh984ckmj0WA0GtHpdEQiEXZ2dmhqaqpIT7bH4+Hx48fAs2it7u7uMo/ox6m8O/iGRCIRFhcXCYfDNDU1YbFY0Ov1FbF/jMfj3L9/vxSbWgwU/6Hy/vtBJpMhlUpRX1/P8PAwFy9efON+JjKZjLa2NlpbWwmHw7jd7leK9jlIit2xnU4nPp8PvV7PwMBAxW1hXubICHJ9fZ0nT56gUCgYHR2tiHIMRSYnJ/nXf/1XpqamsNvtfPjhh1y9evXAIocEQcDr9fLVV1/x+9//HpfLRW1t7Rub80VBtrS0EIlEcDqdpZSuSiGXy5VyPnU6HXa7vWzVyF+HIyPIpaUlxsfH0Wq1XLp0qSJufjqd5ttvv+WTTz55wYFz+fLlA3W7p1IplpeXuXv3Lo8fPyYQCHxv/ZxXRSaT0d7e/oIgU6nUHo747SnG7K6trWGxWBgZGaloZ06RIyHIdDrNxsYGm5ubNDY2MjQ0VPZzpkwmw+TkJL/97W+ZmpoqxabeuHHjwM2mRCLBysoKq6urpNNpVCrVW8VwSqVSmpubaW5urlhBhsPhUlWAgYEBBgcH32oSOigqf4Q/QSqVYm1tja2tLTQaDRaLhZaWlrLuHYudi2/fvv3CynjhwoWyVCtIpVKlDI18Po9arX7roOrGxkZaWlqIxWK4XK43OkLZL0RRxOPxsLy8TCaTYWBgAKvVWhH+hJ/i0AsyEonw4MEDdnZ2GBgYoK+vr6ye1Xg8ztOnT0uZ/sWjjevXr5etdIhSqcRkMjE2NlaKXnrbe6RSqWhsbEShUFTc8cfOzg5LS0ukUilaWlpKeZyHgUMvyOfro5w7d67s9VGePHnCxx9/zNOnT0sROPuRtfE6FEWo0+lobm7m5MmTe/K+xffb3t4mEAgQjUYrwou5tLTE06dPS6VKDlO7wUO9hxQEAZfLxeLiIhKJhJGREVpbW8sylmQyybfffsunn35aMlNv3brFe++9V9asdFEU8fv9rK6uEo/HSzVW94KamhosFgsGg6FUTrLcVQQKhQLT09NMTU1hNpu5ePFi2f0Jr8OhXiG3t7dZX18nlUrR09OD3W4vy0r0fHLx9PQ03d3dvP/++9y4caOsnZTgr9FBv/71rykUChgMBjo7O/fkPhUF6ff78Xq9bG1tYbfby+o8CYVCrK6u4vf7effddw9dd+xDu0Jms1kWFhZYXV2lqamJgYEBGhoaDnzjLggC33zzTSlQvBgNs18pVK+DKIoEAgEWFhaYnZ3F6/UiiuIrVQh4FTQaDVarldraWjweDx6Pp6xlPZ7vjq3X67FarTQ1NR0KZ06RQyvIeDzO+Pg4Gxsb9Pf3c/bs2T170F6VRCLB+Pg4t2/fLjlwiilUlVKMOZ1OIwgC9fX1dHd3Y7fb9yyIXaVSlUxWj8fD1tZWWQXp9/t5+PAh6XSa4eFh7HZ72cbyphxaQYbDYZ4+fYrf76e7u5vh4eEDF2QxuXhmZgabzbZvZTfeBrVaTXNzM/39/Zw4cYKOjo4984TK5XJaW1upra1lZ2cHr9db1pIeW1tbPH78mEKhwOjoaEV0s3pdDqUgE4kEGxsbbG9vo9FosNls1NXVHZhpEo/HuXv3Lp999lmpVOOtW7e4du1axayM8MzBkUgkUCqVjIyMcObMmT33OKrVaurq6pDJZMRiMUKhUFlWyWw2y8bGBisrK2i12jfOZik3h1KQTqeT6elpFAoFg4ODB+pZFUWRycnJUtmNYgTOtWvXKq4BbDabZX5+nuXl5dKeaj+qrDU0NNDS0oIoimxubh54XGuhUMDj8bCxsUE+n6etrQ2bzVZRqXevyqEU5MrKCo8fP8ZgMPDOO+8cWL3VbDbL119/zW9/+9tSClXxnLESS0wWPax37txhY2Nj3zIy6uvrsVgsSKVSnE4n4XB4Xz7nh0gmk8zOzrK5uVmqCLCXpTMPkkMnyGw2y/LyMmtra5hMJkZHRw/k5ieTSR4/flwKFO/p6eHDDz/k5s2bFVf9Gp6t5MFgkMXFRaanp3E6nSQSiX0xJ+vr67FarSVB7uzs7Pln/BjBYJAHDx7g9/s5deoUQ0NDB/r5e8mhEmQ+n8ftduNwOMhkMnR0dGCz2Q7EmfPgwQM++uijFyJwLl26VLG1WQRBwO/34/f7yefzNDQ0YDQake9DWOHLgtzd3d3zz/gxAoEA09PTRCIRTp48SW9v76E66nieQxUYUOzrt7u7S2dn54EEAsTjcWZmZkqB4sXGN9euXasob+rLyOVy9Ho9p06dwmAwcPXqe1itXSiUSkAAIUdWlCNK5ChkbzczF/enUqmUjY2NA10h4/E4DoeDYDBIfX09drv90JqrcMgEWSzHkM1mOX369IG0EZuYmCjVwOnp6eGDDz7Ys8Y3+8maAIkAACAASURBVIkoijQ0NHDlyhVOnx7lzJkxTGYTUkSyfiehcIRQTRuqehMtWlC/hSLVajXt7e0oFAr8fj/BYHDvvsiPIAhCqTu2wWDg5MmTexYWWC4OlcnqcrlK50znzp2jo6Nj3z4rnU7zzTfflPaMzxcxPgwzsMvl4t69e0xNTRFPpNDp61DI5ZBbZ+XuF/zh4y/4j3EHS1FIv2X4qUQioba2tnRfwuEwsVhs3+NaRVFkZmaGmZkZWlpaOHfuXEUEt78Nh0KQoiiSSqVwOp0EAgFqa2vp7+/ft5ufTqeZmJjgN7/5DVNTU/T09PAP//AP3Lx589AEKj99+pR/+Zd/4X/+z//JH7/8E7uhHRBTZDYe8/j//htf/P4rvpn14UzAXhzlK1UqWltbaW1pJhGPs7m5ibDP55GxWIyFhQU2NzexWCwMDQ2VPVzxbTkUgsxkMiwuLuJwOKirq8Nut+9bjGKxc/Gvf/1rnj59WtozXrhw4VCda3k8Hp48mXi2WsVDIImTj3hZfLTI6qKDYDpKopAnI8BeLGQSoK29jfa2NhKJBE6Xm+w+Ru1ks1mcTicul4tCoUBXV9eeRiGVi0Oxhyx2FHY4HPT39zM6Orov4ig6cD7//PMXsjauX79+6GbeVCpFNpdDrdXTa21Dm/ER8uSY9SlIqoy0NtcgGOTIf3BOS5OLRgknBLLSGmp0WvQ1EmRinkwqRy4rIlHIUWqVSBHIxlLUKDU0Nnews+1lZWEWW3sHbVYbMrUKhQz2Uio7OztMT0+TSCSw2Wz7FvRw0BwKQUYiESYmJvD5fFy4cIGhoaF9qQpQPGecmZkpReBcunTp0IkRnhWiampqwtTSymifHal3E3cSom0DGLqWUPi8hBEQxe9bITMQdrK1ts6iM0VQqMdo6aS3t456WZyQw8OWJ0teW09zTwN6McrOgpvdQAJBa2J7fZ25xw8xKTSE3pGi7bLT0iCncQ/tMYfDwcTEBAqFgrGxsbLlwe41FS/IbDaL2+3G5XIB0NfXt+c3P5lM8uTJEz777LNSoPitW7e4cuVKxYXDvQr5vIC5uZUb169wwlbPqb4WNv15YvI62nqbqHM34Qh4iRUKiPDM3gRAhMgKPpeTBWeM3ZyAkE0RWl0j4HQQlp6nvzWLPPCUhekYa/lmTuzU0il1szm7yIrQxlqmlhVfhMDWFPpMGLegQyu0cHHAQOMe+sJWV1dLNW4vXLhw6L2rRSpekD6fj4WFBQRBwGq10tnZuaerYz6fL1WHK0bgHFYzFZ59H5/PTwEJfd1dnLZKMOi1rMbbqDH2MtKWZKe2gFMKAlIkMnhWcLwAmQDbs3cYf7zOeMyGeXSEsZ489dtult1OvLunaa7PYo6v4/WEGQ8WoJBAqVzC75jEKUuzKvTg3E5i3NrEpQyxYxqjpvVv6LEYYI8EGQwGS2ePZ8+epb+/vyJDF9+Eihfk8vJyqT7KyMjInkbwF5OLnz/0v3XrFhcuXDiUYoRnnsep6Sm+/vrP7Gw5ke+0c/rCCRr6TmAdMGOp8ZKTF5BJJSBTIFeCUgrgIbE1xdd3VnjklKM508WJPjvdzXlS4RDqNoFcp5lWYYH8jptwIEFE7CPX0EWNOoRhLYsiEiQvyYBMhUwqIx/PkU9nkCpFpHu0vUskEiwsLOD1eg9Fd+zXpaIFmclkmJ2dZWlpiRMnTnDu3Lk9O5B/OQKnu7ubDz74gOvXr1dsONyrsLu7y7d37nD7s0/we7x47adJCG20Sw3I5X6CsTVW59ysBXbxrD6lbmGEBaWRXtkKu7N3ebAm4tGf4b+9M8x5ez1aCmRHLtEgUaPQyhGe3mHKtU0sbcDYb8N2doCWRIDEQy01Qg2m5iZk9hY0iSYEQYFGW4e9U4lpjyz/3d1d7t27x87ODqdPn+bkyZNHRoxQ4YLc2dlhZWWFQCDA3/7t33Ly5Mk9E8ujR49Ke8ZibOrFixcPtRjhmQNsYXEBn8cLgN/vZOLufzLlnKKgUSAmw0TXFvH6wsS8vyOibKRGuElS6iQ/u0REeQZVzzBtpkaeTX1SlHoDz6KF0/i2fWy44iRU/XQM2hmwimif+PB5BWLadtoH+mhv9LPrMbC9JaNepsZilGPaoydte3ubx48fEw6H+fu///uK72b1ulSsIBOJBEtLS2xvb1NXV1eq3fK2xONxJicnS/0ZbTYbH374Ie+9996R2IfodDp6uns4f/48UomEk+0ttDYZCeUEInmBQo2arEqJUiZDoVKj1spRySDjduNb3yLTcANjtw1TKeYiRzopkBdyqFUePIEQq75a5D39DA830avZwOdzshypI2sdYGzEQo3DwP17UlaRkCmItMpy7EU+TDqdxul04na7qa+vZ2Bg4Mg4c4pUrCDdbjePHz9GEARGR0exWq1v/Z7F5OLioX8xNvWoiBGeBXqfPXsWk8lEY2MjJwf66WhrIycI5AsiQtrB9Ef/wrcP1tkc/pDRX/1X/otFgz6WZCuTIhaJoIlECYU0tDQkIRvHE5AhIUqTapFAKIEr301tax+nWkUaIitM+mJs6vpos5/gbIcK2W6KeeJkClKymQTKROatH7Rid+yVlRXkcjk2m4329vaKbIH3NlSsIDc2Nrh//z5SqZQLFy68tSCz2SzffvvtC2bqrVu3uHjx4pERIzxrULq8vIxEImFwcJCxd95B/sJDqyVl1rGokhEyWWjoNGE1gdpqpKlRSXrmW56EJfzaaaKnrRaDwYjG1Iu9LoWwOYvXu41De4pz7d3Y5XHEp9M4N4NEmt9jqMdOtzZJNhtAGdskE1UQisYIJiANvE0oRy6XY25ujsXFRVpaWjh16tShCWN8HSpyesnlcjgcDpxOJ3q9nqGhobeqVVNMLv7000+ZmZmht7eXDz/8kOvXrx/6YOQioigSj8eZmJjgd7/7HePj42Qyme/+wLk8ktpWGq122urVGHIgiKCwDNM9do7++iwK17fMTzzi0YyDhc0MeaUGfZ0eRUGDtqEVy9kB7HYTdYKEXKoGrcnK0Fgf/V11GORydNpG6utNqKQi6XScSCbH29YqKG41XC4XPT09nDp16sCLmh0EFbdCPh+jKJPJ6OzspLOz861Mk/v373P79m1mZ2dLDpwLFy4cegfO8wiCgMfjYWlpqTSRAd+5b6K0nvZLH3CtN0ay3k5dHdQANJzC8q6Wf9QtMLKZIKkxYTB30N7ejqVdS71OjtJ6kzO6LC2SDlpaaqjRNCEb+CUXmwsM6Hsxt0CNUo/i5M/pfm+XNt+fMMgyqNPbSHPNoHhzAQUCAZaWlgiHw3R3d1dcd+y9ouIEmUgkePLkCZubm9jt9reqPB2Px5mamiodbfT09ByK5OI3oVhNYXV1lVAohFwu/977JpHpaOg+TcPLnb0VTei6mrjQMcRYIk1EqEGh0VFXsjMV0DyErRlspRcZUFnP0vvCbqIGRdsYXRcTdM8FEQoF8kEXmYgF3RtWvItGoywtLRGJRF7ojn0UqTiTNRgM8uTJE3Z3dzl58iT9/f1v/F4TExOluqm9vb2lcLijJkZ45vRIJpNkMhnUajVNTU1vFkQh16OsbaKp4Xkxvj61TS3Y7HZUSgVut5vAduCN32tlZYXJyUnUajWjo6MV0Yx3v6i4FdLr9fL06VNyuRzDw8NvVOw2nU4zPj5eyvR/vgvVYUgufhNkMhlms5mrV69is9k4d+5cWWvEGgx6uqxd+LxeHE4Xfv82AwNv9l4LCws8evQIo9HIpUuXDqzKYDmoqBUyHA6ztrZGNBqlsbERu93+2p60dDrN48ePS8nFfX19hy65+E0oFAoUCgVsNhvvv/8+ly9fLmv+pl6no6vLilKpxOl0sv0GK6QoiiSTSdbX13G73RiNRoaGho7spAoVtEIW66MsLy9TW1vLwMDAa1fZLiYX3759+4XqcOfPnz9UycVvQigU4ssvv2Rubo7z589jsVjKGlJWU1OD1fpMkG63m0Dg9QWZTqdZXV3F4/GUOm2Vuzv2flMxgsxmszx58oT5+flSSs3r7PVisdgLsanFQ/9r164d2kDxV6XYJ/M///M/efjwITKZjNHRUex2e9kOzov5mDqdjlQqRSgUIpPJvFYScSgUYnx8nFAoVBHdsQ+CijFZY7EYs7OzuFwuLBYLp06dei0hPX78mH/91399wYFTCS3hDoJ0Oo3X6yUUCqFUKjEajdTV1ZU9iqXY9ry2tpZEIoHX60UQhFd+vc/n4/Hjx6RSKU6fPn0ou1m9LhWxQqZSKRwOB16vF7lcjtVqxWw2v5Jp8vKhfzGF6vLly4cyufhNkEqlpRVJpVIxODhIS0tL2QUJYDKZaGtrK8WhNjY2vtKRRTFUbn5+nsbGxiPvXS1S/l+MZ57VyclJBEHgxIkTr7z/yeVypepwxZXxH/7hH7h+/fqxESM82ztrtVq6uroYGRmhr6+vYhxYJpOJjo4OMpkMTqeTaDT6Sq/b3t5mY2ODRCKByWTCZrMdyeOql6kIQTocDsbHx5HL5Zw5c4b29vaffE0+n+frr79+obx/sQbOUYrAeRW2t7cJBoO0tLQwOjpKR0dHRayOAGazmc7OTjKZDA6Hg1gs9pOvSafTzM/Ps7Gxgclkor+/vyzdsctB2X81QRBYXV1laWmJuro6zpw585PnZ/F4nIcPH3L79u0XClJdv369Ihvf7DfLy8vcuXMHt9uNXC6vqOprRqORjo4OUqkU6+vrryTI4u/rcDieBciPjSGXV8Tuat8p67cURRGfz8fGxgbRaJTW1lYGBgZ+coV7+PAhn332GbOzs6UuVEctNvVVEUWRpaUlvvjiC7LZLGaz+cD7M/4YdXV1dHR0kM1m8fl8RCKRn3xNMBhkenqaQCDAL37xi32rMliJlFWQiUSCubk5fD4fzc3N2O32H937FbMZXl4Zr1y5cmRjG3+KdDqNw+FgbW0NmUxGPp8v95BeQC6XYzQaUavVJBIJQqEQ+Xz+B1e8RCKBw+F4oTv2UcnIeRXKarIGAgHGx8eJRqOcOnWK3t7eH7y2UCiUkoufT6G6evXqsRUjPDu/lclkNDQ0cObMGUZGRirufmg0GsxmMzqdjmAw+KMNXZ1OJ0+fPkWpVB54d+xKoKwrpNfr5eHDh+RyOc6cOUNPT8/3XpfJZLh79y6fffbZCw6cixcvvnEmyFFBo9Fw7tw58vk8XV1dnDlzpuIEqVQqaWtrw+12s7u7i8fjoba29nvN0MXFRSYmJqirqytVPjhOlGWFFEWRbDaLy+XC5/Oh0Wjo6+v73uyERCLBo0eP+PTTT5meni6tjDdu3DhWpsz3IQgC4XAYlUrFyZMnOXv2bClcrZKQy+V0dnZiNpvZ3d3F6XSSyWS+c10qlWJpaYn19fVSVYDjNuGWZYXM5/Osra2xvr6OVqvFbrf/YAT/gwcPvrMyHofY1Fdhd3e3VJZEEASam5sr0rGlUChob2/HZDKxvr6Oy+Uim32xhkChUGBrawuHw0EqlcJisWC32yvKY3wQlEWQuVyOJ0+esLi4SFdXF2fPnv2OmRWLxZiamiqJsbu7u5RcfBzC4V6Fzc1Nfve73/Hxxx+jVCq5du1auYf0vchkMjo6OjCbzaWmSS8LMhwOMzMzQzAYpL29/dgEArxMWUzWeDzO9PQ0LpcLm83G0NDQd1a8J0+elKrD9fX18eGHH3LlypWqGJ9jZ2eHqakpstksUqm0YlcTqVSKyWTCaDQSiUTweDykUqkXrtnc3HyhymBnZ2eZRlteDlyQgiCwtbXF2toamUyGnp6eF2rmpNNpvv76az755JMX+jMe5eTiNyWfz5PP51Gr1W+UrnaQKBQKGhoaUCgUxONxQqHQCx2WHQ4Hjx49QiKRcP78+VeK1jqKHLjJuru7y9zcHMlkkra2Nrq6ukqmSSqV4smTJ/z2t78trYzvv/8+N27cqNjZv5zodDqGhoZoaGjg+vXrFb+qGAwGWlpaSkECyWQSjUZDLpfD6XTi9/vp7OzkxIkTx9Zhd+CCXF9fZ2ZmBrVazfDw8AvOnGJy8ezsbKnXxvnz56ti/AG0Wi1jY2OcPXuWq1evvlG5k4NEq9VisVjY3NzE4/EQDoeRyWQlR09tbS12ux2TyXQs4la/jwMVpCiKzM/PMzMzQ0dHB1evXqW1tZV4PM7Tp09Lmf5VB86PI4oi4XAYt9tNLBZjYGCAwcHBivc863Q6rFYrwWAQj8dDMBhEqVQyPj6Oy+ViYGCAkZGRYz0BH+geMhwOs7KywtbWFs3NzYyOjqJQKHj8+DH/+3//b2ZnZ0vnjMclufhNyGazrK+v8+c//5nf//73PHr0iN3d3XIP6yfRarVYrVa0Wi1bW1tsb28TCoWYnJxke3ubwcFBTpw4gUy2l83PDxcHtkImk0lWVlbw+XzU1dUxODiIVqvl4cOHpeTi4jnju+++e6zyGV+XVCrF3Nwcd+/eZWJiorQfHxwcRCaTkU6nSyUhM5lMyQt74sQJzp49W7aJrhibqtPpSm0BionIEomEgYGBYxcq9zIHJki/38/4+DjpdJrTp09jNptL1eGKETjFFKpKN73KjSAIxONxZDIZWq2WeDzOV199VWpEk0gkiMVixONxYrEYXq+XZDLJP/7jP9LX11c2QRZD6GprawkEAjx69IhsNosgCFgsFqxW67E2V+EABVmMW5VKpQwNDeF2u5mYmPhOef+qGH8alUpFd3c3169fx2azIZfLaWxsRCqVIggC9fX1mM1mBEEgFoshCAKzs7Ps7OyQy+XKOnaNRlM6npmZmQGepWgNDw+XtY5spXAggszlcni9XlwuF3V1daU0qoWFBfr6+vjFL35x6DsXHySFQqHU98Rms9HS0kJtbS3JZJJ0Oo1ery+d+fl8PhobG9HpdFgslopI9DWZTJhMJqamplCr1Vy9epV33nmn6jPgAARZbAKzublJLpfD7XZz7949UqlUqVTj+fPnq2J8DQKBAH/84x/Z3Nzkxo0bDA4O0tTURC6XQxAEFAoFarUaQRAIBAJIJBK6urqw2+0VYYHU1dVhMplIJpOEQiE6Ozs5efLksTdX4QAEmc1mmZ+f5+nTp6X6nFqtlrNnz/Lzn/+cK1euVMRDclgoOkG+/fZbdnZ2OHfuHHq9/nuzIvL5PC6XC6/XS1tbGwMDAxWRPaFWq9HpdMjlcpRKJWazuerE+wv7fuwRi8WYnp5mYmKCSCRCQ0MDg4OD/N3f/R3vvvtuVYyvSSQSweFwsLu7Sy6XQxRFCoXC916bSqVwOp0EAgEaGhpoa2urCJM1mUwSi8WQSCRoNJqqqfoc+/7reL1epqenWVlZobW1lbGxMa5fv86JEydQKBQlp0OVH0cul5dWvPX1dSKRCAaDoWSaRqNRRFFEFEUkEglKpRK/34/X6yWRSKDT6Uoe2XLcb4lEglwuRxAEnE4nS0tLRKNRMpnMCzGtx519FWSxWNHc3FzpQdBqtWSzWSYmJshkMj84u1d5EYVCQS6XY3Nzk6dPnxKLxaipqcHlcnH//n0KhcILgqypqcHj8bCxsUE4HGZ9fZ179+4hCEJZ6u5IJBIUCgX5fJ779++zubmJVCqtiBW7kti3uyGKIg6Hg4mJCTY3N4FnjTenp6dxu90UCoXvzRqv8v1IpVIKhQKJRAK/349MJiOVSvH1118zPT2NIAgvrDQKhYJEIsHm5iaZTIY7d+4wNzeHIAhlmwSLxzLhcJja2loaGxvp7e2tmqzPIRH3yV4QRZGZmaf86U9/YnJygng8hl7/zMTK5XLVlfENKbYNkEqliKJIPp//3nspiiJSqRSFQoFEIiGfz5d9a1Acp16vp6mpCY1Gg8Vi4Z133sFms/3Eq48H+yZIgHgiQSQSIZVIUCgUkPwl5/Hl2fzII5FQzF142+8tlUpLovwxQT772Gf7NolEgiAIZRdk8bsrlUpqamqQyeSoVEq0Wm3F1QEqF/sqyCpVqrwe+7ujTvvJJeIE8kaoqcVsqJB2W1UqDrEgUBClSGV/tSaOI/uojxzxlQk2ljdY0J9F13uWd2rAeDwqwj+HSD6dJBlJIarUqGq1KCWS8jdVKSe5JNlUnEQWsqIcGTnEfIG8RI2qtp66mgpoOlMm9keQYhoxtMjCnS/55kkAz6iFk72QP3ZTXwZia6w/dTHrkKLtsjN4xoZZcXwfOABEkUI6QtixzPpWCH9Wi1zbSJNBjkomBaUOvakZY5ORxhpQHqPnZn8EmdkitPwND+5N8eWinroBKe/oQXnc8k7T26SWv+Th7yf5fLGdrr/R0nTaRtOxsxJeQq5GJi+QWrvD7J8nuJMbobb/Hd6zpJFvzrO8mSFpu8rQ5av8rM9A8zE6FdnjiVoEdklE1phf2WB2JcFuRI1KpaJWD4pjNNNBmFxokbmn09y9v8jc/Ba+YJKU+OwuHWukMqRKCentTXbWVvHGZGQa22lqbae9PoUmOMXjb+7y5Z0ltoOpn36/I8TerpBiCiHkIODdYiOtJClvolGjp0mnRKM8TmZaHiHqIuBcYGEnR0CsQ6+qoV4pRSb5IUEKFHI5coIEpHLkChlSCSAKiCIURAkSiQSZBJCIFAogIkUq5ZkTRBQoiBJEJEglEiq7RpSAKMaJJBRkZVZsQ2c4f/UdznQI1NYuIDhm+f03bhyLLhIxO3B8MoH2UJAFsqkIm/M+ApEY6gYNtR2NxF06ahRyajg+ghTFKJsLWzgXg0jqa2nuVxCbVaESC0hEEb7Pjxh143O4cIUgo2vD1N5GmwHU2V3CkTg7aRUSZS2ttQI1hRie7TwJZSPNHQ00KmJkd7y4dqWklfW0NtfSoKlkf3aIQnILz66UnUIP7d09jHXLaEIGQppkOExaMKNW60F+vOz7PfvVxJSfiMfNuk+OVN1IV3OSpWYVjh0NEpkCDXAstpDZIMntZdYcSfy5Vjp7tMRiPryrMoR84TurYyGxS2zHg8fjxeP3EorF8ecDKDeTnB8wYq/xElyaYcYnJ1bbR7dJpD7uYnE+QtTQSd+lXjp1QUKzs0zO5knX9zJ2fZiTnbWUP9HqB8gHyPqW2dxJ4kw2UR/zknJoWciFCE0EWMx20jV6lq4LPTTWH6MNJHslSCFLyrFMwOEhqLbTZKqhLutEUciTUWtRKJVo9+zDKpus18H20gLbtEJvF20tC0RmPagkUgoiSCTP2wlBAvPf8PTRMguFDnRWM72dGcKzDuaW87RpTtFlTZBaG8exlMLRnMe3q6bRM8vaAweJ+lYiml02TRm2n0wz+WWUQlsa7XAXLZ21aKhQqyS8S3xjne1kFL9Ez+7aONOf3eUrT5jdhBpV1/vcOHuOsydbaa09FtN4ibfXiJiCmIutjTXm1+PsmEyoI2G23Fu4A0niKg1KtRodFfpw7BWFFGTDBPwB1nf1aCwn6BszYRf8bEmkKCRyFGo1NWpQAaS2yfoeMD0xyd0VJfS00WfvpKdBhRjzEM3oMBhUFApZoltb+NfieJUR6tpVNNTkyMR8eHaysNZBjUaORJYhHosS90dJpZ+FyFXqNjIbCOBbdRGXazGcGKajQ4kxPY1/fZqFZD+17R1c6rAwaFZxvAzWvRBkeoeEb42teIFtaS3SVBghvoh7zYUzUkOqQYe6Rl255tNekQsheB+x4tpmItRJR4uUhrSXeGwbXyhOPK1EEw4TDGWJG2Rotpdx3/2/TDqUbLbe4PrYKS7aVGjkShix0tCrobVNSmY9iicAwWQjWoOZwYEmrE31+B7qWdlsRCJrx9YooLfVsmRXkle00VSjppFKFWSekN/P+kaYnLafwesf8N55NafjBqzCJu4/bbE8s8DSWTsXei20lHu4B8xbCjJCPBTBsVkgr++i12qmViaiD+7g35ZRo1Uh0dWiUak58nUB0hEiK09YfLDAn9Ya0Tz6iqUvUwgpJ3MTDhY2VKwJIjXNCjJ/a6N528HS+Bb+wkmMV0/QM1CLXgXQirldglkCsI4j7GHNKyWmsNHX081wSwqVP0osKydZ10Wz1Y7dsIHgSiA3mlA22DHpdVRmIzcBCLDt32HVIUe0tdAz0o69CxoKQ4z5n2C/P87c0jQrKyOsXLFQq4bjtIt8K0H65r5gfl3NWrAJy6Cdc2PNGApp0osL/39797LbxBUGcPx/Zuzx+J442LETJ05CLpALCbT0CkUti6ot6uVB+gx9iy76Cl120xUrWmgrKhFxCSUE50qIgxPb8TXjOV2AkIrUVVR6lHy/5Swsy9Jf+ubMmWPadzrQqtFsNqk22jQ9jRs4xvsUtcOhjhG2usQOizxbLXJr+xAOy2xvltg7cNGbTykur1L6IEjr2Q6Ly0EOx9LMTveRe3WkjIfWFp7vYTdXqG6vsdrpgaF5ZiaHGOr8yvJfT9hsRglOzTI5laW3fYellW3awQLJ0SGi0bChv3MbuivslqsUa4M4iQHG85AEsEKEYhFc28evV6nXWxx04c2/Sv3/OlKQP3//Aw+c99kb/YreSIa4UihVYW+ryN2lNVZXAux762zs7LFZz1JIBo7vPUEkQ3zmcy6lLlAot6i1u2hdgcoiv1+/z/XbLon5K3z29UUuDjZZv1dmr+TRyDuEI9bLCcKD2jOq3Ri1Q01sa5X9pyX2+kaJTc9zJu3ibqzydGOXTvpDhhfmmMiE0IvP2VyvYaeCpPMJrOCLBSTLtCr9A9h+ROl5jTUnz1h6kIkE9ALU9ilvbFGq+zST/fT2Jck5HP/J6jVHG1ntflKZLKmxPtI9Nhof2h06zimCI+/zth/g7ECe0+nQ8d+d4sSJ5GcZz88y/uriARyEsLfrLC655Kfn+eDyW0yxBmGLvtAO68U/+OWnAl4hzmRY4SqF6h8jZLVoLz1mbaXEYe4KuXMjZJxddu4/4eGKhzMxxvTFAbLRNXZXi9y/X2Z3okKv36BFgi6WQYtoGu01aGw9YOfGDW4vLvOwcZ54tczzB4ssMQ5RrwAAAnhJREFUtQ7YX77J0s0S27FJps5d5t25QUaCcNLekjxSkJ9++x2em0TFUiRiYKEglCG78AUfj13h7bZCOzGiiTjJqH0iHnv8kw9+ANtxicRDhB3QKCBHenCYmRnFg8U/+e3HLlu5U5wZGyYzOsd82mUqWqfS6FBrueTODjBxOoprP6ZYtqh5QwwX8sxMBIiqCuuNFnv1II2qh27WQGXQypwcQaM7VSobT7h3d43VnSo62KRdWePRrQ2K+5s8Xt5iozJIz/lLXL16ictn+ziJf897pEZyE2dfu6LAcnGTLm6yn/RRPvxYsMAap3AhyJexAPHxAVI++JZDYvQdLn5zQD3/hMVShEBPhmx+hIGhPNlkmJ5oAmv6I2ZjCwyPTlHIKqJ+L73zV3kv1cVZmORMCCI6Se+ZS7xzbZzJ/imGh+PkwsqwTRgKZYcIpcZIL1zjk0yH+dAQmf4+CtEm3Z4oKjZKzsmTn55jfi5L3j3mj8n+hZwY8J/SoH26XZ+uD8qysQMvR0ndRXs19p+VeL7XpuP2EE31kYo5RBwbW2l8z8P3NdhBLFthaZ+u18X3QQUD2JZC0aFRrlKvdyASw03GCNsWAdPuH7WP73dffH8NWlkopbB4cVqerwEVwA4GCJ7EEl+SIE3ge2grYOjKqHiTJEghDHKChwMhzCNBCmEQCVIIg0iQQhhEghTCIBKkEAaRIIUwiAQphEEkSCEMIkEKYRAJUgiDSJBCGESCFMIgEqQQBpEghTCIBCmEQSRIIQwiQQphEAlSCINIkEIYRIIUwiASpBAGkSCFMIgEKYRBJEghDCJBCmEQCVIIg0iQQhhEghTCIBKkEAb5GzGqEaobRKivAAAAAElFTkSuQmCC)
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,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)
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,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)
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,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)
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==)
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,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=)
From the fig. segments shown are tangents then x =
![](data:image/png;base64,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)
maths-General