Maths-
General
Easy
Question
If the angles of the Δ ABC are in A.P then 3R2=1
- bc
- b2c
- abc
- b2
Hint:
The angles of the triangle ABC are denoted by A, B, C and the corresponding opposite sides by a, b, c.
The correct answer is: b2
s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.
Related Questions to study
physics-
Two circular loop A & B of radius rA and rB respectively are made from a uniform wire. The ratio of their moment of inertia about axes passing through their center and perpendicular to their planes is
is equal to...
Two circular loop A & B of radius rA and rB respectively are made from a uniform wire. The ratio of their moment of inertia about axes passing through their center and perpendicular to their planes is
is equal to...
physics-General
Maths-
In ![straight capital delta A B C comma c left parenthesis a cos space B minus b cos space A right parenthesis equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMwAAAARCAYAAACRgkMDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAABIlJREFUeNrtWn9EnGEcf52TmYn7I8nJmCSTHJMkmdEfc04SM5kkMZOZTGSSmYxkZmb/zCT7Y+LkZGYic5JkzCRzEvtjf2QSmZNkjtv30ed4PPs+7/u8975vd9fdh6+6533ee5/n83x/32tZ1YdxkjmrhouOOZx1DR7QQbJVo6FqsIkzDxyrJCGX90w4XD8lyZH8IvlJ8pGkiZl3jWSeZJvkBPNnSSI+ERir0MM35c8rToo4+1JDp3s3SDaCfvgQSZZkxMU9d0n+koQ111tgADKEESwqY5Mkn0h6pUNrBiGLHvcVg8FUIkz58+M5OxXGjZPubcBwAoMgbIBk13B+BPes4T4OYvyDMjaojE2RvAtwXyJqPaxQgzHhz6/nLFUQLya69yjImlUmbAXRxglvMU9EpDeaOU9hEDLek9zG/61IM8Ie138FhrEPr5OSUrlVRC4VIpI9IznAPcKTX2Xm9ZCsIzUSadGwcj1BksF3iL/9mnQzjbQnDzGBE39+QTxnGnz8xl7TmtSvlHy40b1uki9BGcx3kjYp/3MKz91IoQQaofQckjDGEFKjBSXvfGFQA5kYi1j/c5J6kjqkeAlcz2JMhVj/axhWSFqrms4dSntoVbx7F/bejs/t+NytfM83jeI4wYk/v5DEuqckPl4yUafUfLjRvTqcPYe8gWgRJ1lWxtI2Gwpjw80ag5OxJy3gmPGMGeTPXjAHxdchp6nXkoznjitjywjtOixLhil72BWmoC6meeHEn18Qz7mujNUzCldqPtzonoUo5zu+Mi24XixEF74nlTHh3ceZlOdYsvY+66y12ypdP/W49hA8XsSlwaQZr7fOpGRZKI4OXPTiPNsAGg9DLvdmx59fXjMEBVZxidlHKflwo3uBGcwtKbyp2MIhyWjTGNJN66zdaSnhWc0h76HWcAqZpui0nNuH3CGqLVRZOVUltEPexUFdQXMjY6P0bvjzC11wICY1QCn5cKN7gaVkmzatt4T1/499GzYPUFt8Q8i5ZQwrHTGhpJc9HHYcBb4d1lCoyjhkClnuMA598qgynthEb8slf35APIdrUz8mmSkjPtzoXiBFfw86SHbISB2m+ySvbOYuKTWAqCtGlTkLShheYEKsGwhjd2qDc23lfaQcBcwwdZwF5XTK2fuZdCPlkGqZpAom/PkB7jl1aPw0lQkfbnXPwpn7Go3TCMd2GJHaizsIozqMKZtKSUVqA8kd66x1K3sgUTMcwctEpNw5AeXoU0jJM52sbeSxYXi/CSWicD9czqI1GcIaRKfns6b9KVqng5gbVbx+J7o0hYK5A597HHhKG5yPCX9+IIWiv8B1FGOjZcJHMbpXiEi+/nCZdyFJpvuhIgriCziS7j+FwkeZ+1rQocpi7h94qjjjRTiDaUbBngOxY5p6TG1sTGNfMzDSA4v/ESyGxkgOCtvPpK678JI/NN9R4CEHwzR5tcWUP684wJ72pD0O2Mw/bz6K0b1zeTWmEsCFXhOYvHzZUKP3wuDcXr4sZ8TgsYp9K+CBVXu9vxowj5qn6iHCbmONhhpKgX8EN5M9FDQlBgAAASN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4Mzk0OzwvbWk+PG1pPkE8L21pPjxtaT5CPC9taT48bWk+QzwvbWk+PG1vPiw8L21vPjxtaT5jPC9taT48bW8+KDwvbW8+PG1pPmE8L21pPjxtaT5jb3M8L21pPjxtbz4mI3hBMDs8L21vPjxtaT5CPC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT5iPC9taT48bWk+Y29zPC9taT48bW8+JiN4QTA7PC9tbz48bWk+QTwvbWk+PG1vPik8L21vPjxtbz49PC9tbz48L21hdGg+xSqrvwAAAABJRU5ErkJggg==)
s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.
In ![straight capital delta A B C comma c left parenthesis a cos space B minus b cos space A right parenthesis equals](data:image/png;base64,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)
Maths-General
s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.
maths-
In ![straight triangle A B C comma sum fraction numerator a squared sin space left parenthesis B minus C right parenthesis over denominator sin begin display style space end style A end fraction equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMMAAAAmCAYAAAB59i+bAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAaPUZr5AAABSZJREFUeNrtnH9kVVEcwI95MjMxmXkykcz0R0Z/ZJIZM0mSSJ5JMpJMkpEkmcRMJtM/kyf9kZHMTBKTmUn/JDPZH7E/kv6YmMw8M4/X+Xrfy3F2zj3n3HfPvfe99/3wNe++8+497v1+z/n+2mWMSJIKyj6XL1xO0C0hmp0WLne4fM/AXGAekxm/X5M4T6KB2Uv5+qe4fK2Te/UF50s0IANcViK6WnEqWF+IoZa5/OKyyWWRS97j/TjOZYrLGpcSXvcplw78/jSXVVKbxiOPing8RWPowzmoOIFKKQKK+drT/Rjn8oHLOXQhgW4u96RrrqJREA1CDz74fMrzgFV4TPPdZS5vpWNXFMfi4AGXV5Zj79ZBfEPgijbBZYtVs0Wwsh5T7AgfuRwOcRWW0U2oaHaBiubzVXRn9tD96jbM9xOuxCqeoJKKvOFy3sPCAHPOWY7v5/KZVC37wGo/gz4uGMY7XGFFwBB6Q87xjcslRzepgoYwJRjfTYt4ZIfLIc13wdxb0J0qossSN88dz3sI501kmAIqkLySXlAoriwiJSFgdDGGQcUutW84Tznku5/C/HY97AgBG8y91rJP6pZtlnELF1lRuEkmLmNQW3A0hiiBdjnE3dsVVuIhVk2/9oRcxyS660RJLZMx1EilRjFRErIgskK50o4B5YZGAeMyBp2bdEbhl4+gGxYnUVwecpPqwBj+Sp/Pstqryw8154jLGJZwniqXrygdu+6Q8XEBFow2h/EUQMfAqKDY0xEMycQfLq3C58dc3tc4Z53fH5cx6FKrMxiAixQNrltU4LzjDuPHPOxQTckwbrGgJIuS8tZqDFCQmkUFhjgB8vEfYzDgZY/GoCu6zQsBcyerZqrWmD7zVAtwr7ZxFwwSB/BcLqKhDEnjUy26DWGQM1jDOUypM9uyv6lcb8NJXMVBUb7hw46LR5hReowPdIsdTK3aunNlNKa8R2NgGBjL/T7bwjzg2cxxOepRxyCb9EZYqP7hripn4lJtx4BVbh0NYl0KEG25hlt9LuRG2JT9bcv1NnShIcCN/40G4oNOln2oUc+S+6xaUWX4d9zx9x1oREshK6RN2d+lXG9LG+5AwUo03MTu422W/RYH8AhupXXxI6ya2msTlGcDj9syi0HXDS4vNWNMZX/Xcr0r04JbMkphFaFT5BHpWAGP29CPbk3glmxqxpnK/q7lelcKgn9cpMfeUMSRMg9t7bXx23Lok4uNYpAvV/XkmMr+Ucr1LsH0jhBMt5L+EC4KH2YoousjxxfP2MF/2zOV/aOW621oFwxxm5k7PKOuPCT+xavbYHKFglhARS9TV00HMGAVMZX9fZbeF4SbOUzrH7lJqgyLTZAM3//QuBWrIReWU6w2ZX/Xcr0ND4Q5PSGdIVRAfv++5VhwgyakY5D6ehHyGyjeiIUUm7K/a7nexIBgCB/okRMqoLq7xuwLay04PvgfXqiUrqMvrmNUMhabsr9LuX4OlVxX04Aq6haO2WRulWuiiViIGLzM4+/foYKGcRSD1gDbsr9tuT7MGHIYnMP3JeZWyayQehD1yJzCSIKgPzC8kQiBWL0GkD65R+qWXfowsM9FzCykkr6rU2Mw9ZwRKQMuVleIYjSbMfjCpueMIBJNeCT1ShmVy2nqOSOIxEjylTIitj1nBJEYSb5SJsCl54wgEiPJV8oE2PacEUTiJPVKGcbces4IIjV8v1IGcOk5I4jU8P1KGdeeM4JIDZ+vlInSc0YQiZLUK2Wi9JzVLf8BDzpZtKmQDxEAAAGQdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiYjeDI1QjM7PC9taT48bWk+QTwvbWk+PG1pPkI8L21pPjxtaT5DPC9taT48bW8+LDwvbW8+PG1vPiYjeDIyMTE7PC9tbz48bWZyYWM+PG1yb3c+PG1zdXA+PG1pPmE8L21pPjxtbj4yPC9tbj48L21zdXA+PG1pPnNpbjwvbWk+PG1vPiYjeEEwOzwvbW8+PG1vPig8L21vPjxtaT5CPC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT5DPC9taT48bW8+KTwvbW8+PC9tcm93Pjxtcm93PjxtaT5zaW48L21pPjxtc3R5bGUgZGlzcGxheXN0eWxlPSJ0cnVlIj48bW8+JiN4QTA7PC9tbz48L21zdHlsZT48bWk+QTwvbWk+PC9tcm93PjwvbWZyYWM+PG1vPj08L21vPjwvbWF0aD7uUPmhAAAAAElFTkSuQmCC)
In ![straight triangle A B C comma sum fraction numerator a squared sin space left parenthesis B minus C right parenthesis over denominator sin begin display style space end style A end fraction equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMMAAAAmCAYAAAB59i+bAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAaPUZr5AAABSZJREFUeNrtnH9kVVEcwI95MjMxmXkykcz0R0Z/ZJIZM0mSSJ5JMpJMkpEkmcRMJtM/kyf9kZHMTBKTmUn/JDPZH7E/kv6YmMw8M4/X+Xrfy3F2zj3n3HfPvfe99/3wNe++8+497v1+z/n+2mWMSJIKyj6XL1xO0C0hmp0WLne4fM/AXGAekxm/X5M4T6KB2Uv5+qe4fK2Te/UF50s0IANcViK6WnEqWF+IoZa5/OKyyWWRS97j/TjOZYrLGpcSXvcplw78/jSXVVKbxiOPing8RWPowzmoOIFKKQKK+drT/Rjn8oHLOXQhgW4u96RrrqJREA1CDz74fMrzgFV4TPPdZS5vpWNXFMfi4AGXV5Zj79ZBfEPgijbBZYtVs0Wwsh5T7AgfuRwOcRWW0U2oaHaBiubzVXRn9tD96jbM9xOuxCqeoJKKvOFy3sPCAHPOWY7v5/KZVC37wGo/gz4uGMY7XGFFwBB6Q87xjcslRzepgoYwJRjfTYt4ZIfLIc13wdxb0J0qossSN88dz3sI501kmAIqkLySXlAoriwiJSFgdDGGQcUutW84Tznku5/C/HY97AgBG8y91rJP6pZtlnELF1lRuEkmLmNQW3A0hiiBdjnE3dsVVuIhVk2/9oRcxyS660RJLZMx1EilRjFRErIgskK50o4B5YZGAeMyBp2bdEbhl4+gGxYnUVwecpPqwBj+Sp/Pstqryw8154jLGJZwniqXrygdu+6Q8XEBFow2h/EUQMfAqKDY0xEMycQfLq3C58dc3tc4Z53fH5cx6FKrMxiAixQNrltU4LzjDuPHPOxQTckwbrGgJIuS8tZqDFCQmkUFhjgB8vEfYzDgZY/GoCu6zQsBcyerZqrWmD7zVAtwr7ZxFwwSB/BcLqKhDEnjUy26DWGQM1jDOUypM9uyv6lcb8NJXMVBUb7hw46LR5hReowPdIsdTK3aunNlNKa8R2NgGBjL/T7bwjzg2cxxOepRxyCb9EZYqP7hripn4lJtx4BVbh0NYl0KEG25hlt9LuRG2JT9bcv1NnShIcCN/40G4oNOln2oUc+S+6xaUWX4d9zx9x1oREshK6RN2d+lXG9LG+5AwUo03MTu422W/RYH8AhupXXxI6ya2msTlGcDj9syi0HXDS4vNWNMZX/Xcr0r04JbMkphFaFT5BHpWAGP29CPbk3glmxqxpnK/q7lelcKgn9cpMfeUMSRMg9t7bXx23Lok4uNYpAvV/XkmMr+Ucr1LsH0jhBMt5L+EC4KH2YoousjxxfP2MF/2zOV/aOW621oFwxxm5k7PKOuPCT+xavbYHKFglhARS9TV00HMGAVMZX9fZbeF4SbOUzrH7lJqgyLTZAM3//QuBWrIReWU6w2ZX/Xcr0ND4Q5PSGdIVRAfv++5VhwgyakY5D6ehHyGyjeiIUUm7K/a7nexIBgCB/okRMqoLq7xuwLay04PvgfXqiUrqMvrmNUMhabsr9LuX4OlVxX04Aq6haO2WRulWuiiViIGLzM4+/foYKGcRSD1gDbsr9tuT7MGHIYnMP3JeZWyayQehD1yJzCSIKgPzC8kQiBWL0GkD65R+qWXfowsM9FzCykkr6rU2Mw9ZwRKQMuVleIYjSbMfjCpueMIBJNeCT1ShmVy2nqOSOIxEjylTIitj1nBJEYSb5SJsCl54wgEiPJV8oE2PacEUTiJPVKGcbces4IIjV8v1IGcOk5I4jU8P1KGdeeM4JIDZ+vlInSc0YQiZLUK2Wi9JzVLf8BDzpZtKmQDxEAAAGQdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiYjeDI1QjM7PC9taT48bWk+QTwvbWk+PG1pPkI8L21pPjxtaT5DPC9taT48bW8+LDwvbW8+PG1vPiYjeDIyMTE7PC9tbz48bWZyYWM+PG1yb3c+PG1zdXA+PG1pPmE8L21pPjxtbj4yPC9tbj48L21zdXA+PG1pPnNpbjwvbWk+PG1vPiYjeEEwOzwvbW8+PG1vPig8L21vPjxtaT5CPC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT5DPC9taT48bW8+KTwvbW8+PC9tcm93Pjxtcm93PjxtaT5zaW48L21pPjxtc3R5bGUgZGlzcGxheXN0eWxlPSJ0cnVlIj48bW8+JiN4QTA7PC9tbz48L21zdHlsZT48bWk+QTwvbWk+PC9tcm93PjwvbWZyYWM+PG1vPj08L21vPjwvbWF0aD7uUPmhAAAAAElFTkSuQmCC)
maths-General
physics-
A cylinder of mass 5 kg. and radius 30 cm, and free to rotate about its axis, receives an angular impulse of 3 kgM2 S-1 initially followed by a similar impulse after every 4sec. what is the angular speed of the cylinder 30 sec after initial emulse ? The cylinder is at rest initially
A cylinder of mass 5 kg. and radius 30 cm, and free to rotate about its axis, receives an angular impulse of 3 kgM2 S-1 initially followed by a similar impulse after every 4sec. what is the angular speed of the cylinder 30 sec after initial emulse ? The cylinder is at rest initially
physics-General
maths-
In ![straight triangle A B C comma sum a cubed sin space left parenthesis B minus C right parenthesis equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALsAAAATCAYAAADI33zpAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABFtJREFUeNrtW29EnVEcfl1XZmZkkmQiSfowsQ8zk0RmkpkxcyWTmElmEpOZZEYymexLcmUfJjLJZEYmSfYlk0wfRh9m+pCRTJJc7s5Zz2vH2XvOe/6+3ep9+NH75773nPM85/fvvgXB2UDR0lKkSMWu+L2HxNaI3UypSOEbPYzwxgwE6wINxH6UwFr0Ehspcb5GMM4UhqBe9TfE+4HYuYTFniG2c8xrcIXYlxPC1wrGmxjaiB0Qa7V4xpOY6/T5BXi9TQixKuK+WmKjSAf2cf8LYuUaY2kktgUBrxKrSGgdLxF7Q6zbMBVyKaAmSx5cIY7Pq8SWkxI69UTrEPw6jnVxH/lqVnC9DpNlQSc8xZ0bIDZPrJkZx2VspCnNMVVC6FREP7EBkqgXuiw+7wJNELsND66gyucyRO8d/cSG8fcwBqiDcmySBWJ3BPfQ8++4c3e5c0+JTTqe23l4Liqk3QQKx4vEXhJ7eIxpAfWifRY8uIIOn4+TqC9o2N2AKEJxbOC8KiaI5Yg9QAiPwhAmz+ItsVv4ux4hNetpnmMQfAFFrG7ko05gm+m21CikbHwoX0QYF3V+ioLje1gb+swleEYZPsGTmvDgCrp8Xif22bfYqVA7uXM5nFcd5DyTNmwK7puBV8kgzOa5HP+VQs5vgxwjsrzmZ+n8xhHBMsxcRGhG+sSCHt/WTGOKEPoos7m6IXgZaHFeZsiDK+jyWYZxy9JDq5axLLdTqZCzIJH1NF+Do9Ybj+/MwPYiPMkG8kkfaGS6M6sa3Zlwk8xEeMJ2ASEH8Ky8599XKLCjxN4aEWUOY55TkFyL48EVTPg89OjspIKWbQQ2JPL5Pc1XeyMI2mN2cBvaYvXM9QNPc7zAELyjkALwWET0YrGkkMZE5cor2Dw6YjcpZAuSdEzGgyuPasqnN7GrpCoTEnIa4MV5tKAgZHEtIh/rRHiOC2G2mGOIMSlO97nuFCsYk403Ca9X71HsojQmjgdXMOHTWxqjWoTS698EYX9Z8sV8CzIXkSd3cZX6HlMku+wGhGMaMnzGL+74hmCT62BQ8AxXYl/AOKMcXBwPrqDLp7cClfZV+xXvHQj+tSVD0Lbaa8lnprmcdjz4/0eWPBc18oF+y1OGFkbo8xbP2eI2+3Ni7y3HJsq7XYld1HpU4cEVdPns8xBh/rbA1gL1H44yuL8Wx/SXtnWEZBF6uM0wyxRCFegwrHGhtgY59SBTyFGRdWDh2rjNVJR0RKqDozZhEd2hckvHMIF1oGOk/eiPlhz0oBbwJXZRvaXCgyvo8BlmCs5/VJoLzN4GnGVaVx0x31GNojDEDtetmMY9POrQ6Qg7J7vwou0RkUMk9iyKriLybZ13LkQieoZ5Pwdh24G89SjLOwvYLFUexR5gDfi5q/LgCqp8Jvq6wEnEdMSihUV1SGingSBVUHEC1id9EeyUoAmFc9awcj8r/7zxKCj9V3xHg+N9taLkQUNvpUWbKv1PpVOOP89BrWBN+EKIAAABHXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj4mI3gyNUIzOzwvbWk+PG1pPkE8L21pPjxtaT5CPC9taT48bWk+QzwvbWk+PG1vPiw8L21vPjxtbz4mI3gyMjExOzwvbW8+PG1zdXA+PG1pPmE8L21pPjxtbj4zPC9tbj48L21zdXA+PG1pPnNpbjwvbWk+PG1vPiYjeEEwOzwvbW8+PG1vPig8L21vPjxtaT5CPC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT5DPC9taT48bW8+KTwvbW8+PG1vPj08L21vPjwvbWF0aD4hqiw2AAAAAElFTkSuQmCC)
In ![straight triangle A B C comma sum a cubed sin space left parenthesis B minus C right parenthesis equals](data:image/png;base64,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)
maths-General
physics-
A body of mass m is tied to one end of spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is one centimeter. If the angular velocity is doubted, the elongation in the spring is 5 cm. The original length of spring is..
A body of mass m is tied to one end of spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is one centimeter. If the angular velocity is doubted, the elongation in the spring is 5 cm. The original length of spring is..
physics-General
Maths-
In ![straight triangle A B C comma a b c sin space A over 2 sin space B over 2 sin space C over 2 equals](data:image/png;base64,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)
In ![straight triangle A B C comma a b c sin space A over 2 sin space B over 2 sin space C over 2 equals](data:image/png;base64,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)
Maths-General
maths-
Let n be the number of points having rational coordinates equidistant from the point ![left parenthesis 0 comma square root of 3 right parenthesis text , then end text](data:image/png;base64,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)
Let n be the number of points having rational coordinates equidistant from the point ![left parenthesis 0 comma square root of 3 right parenthesis text , then end text](data:image/png;base64,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)
maths-General
biology
Both sickle cell anemia and Hunington’s chorea are :
Both sickle cell anemia and Hunington’s chorea are :
biologyGeneral
biology
HIV that causes AIDS, first starts destroying
HIV that causes AIDS, first starts destroying
biologyGeneral
biology
A very much publicised treatment method ‘DOTS’ is being adopted for the cure of
A very much publicised treatment method ‘DOTS’ is being adopted for the cure of
biologyGeneral
biology
Sickle cell anaemia is due to
Sickle cell anaemia is due to
biologyGeneral
maths-
In figure,
and
then the area of the shaded region in square units is
![](data:image/png;base64,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)
In figure,
and
then the area of the shaded region in square units is
![](data:image/png;base64,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)
maths-General
maths-
In the figure,
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The value of
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![](data:image/png;base64,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)
In the figure,
and ar
The value of
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![](data:image/png;base64,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)
maths-General
maths-
The median AD of the triangle ABC is bisected at E and BE meets AC at F. If AF:AC =1/k then the value k
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPsAAADaCAYAAABggjQ1AAAgAElEQVR4nOydeZSV1Znuf2c+p+Z5LmpmLIpmFEVUwAGvBGQSouDUaEeTGNNJp9Pd3raT26bTw01fO2ulk44maaeoMaQDioiKzPMkVRZjgQxFFUXNVWee7h+sd7PP0WgRK0UVfM9aLKY653zfd/a73+l5n22KRqNRDBgwcNXDfKUvwIABAwMDw9gNGLhGYBi7AQPXCAxjN2DgGoFh7AYMXCMwjN2AgWsEhrEbMHCNwDB2AwauERjGbsDANQLD2A0YuEZgvdIXcK0hEAgQDAax2+1EIhEsFgsAJpMJs9ms/hyNRolEIjGvNZvNmEymAb9mA1cHDM8+wBCDDQQCyFhCOBxWxh0KhQiFQugjC/F/ll8GDFwODGMfYFgsFiwWC6FQCLPZTDQaJRQKEQ6HiUQi+P1+vF4vkUjkU734p3l8Awb6AsPYBxjhcJhQKITFYokx5kgkQm9vL0eOHGHTpk14vV7lvfXfDa9u4I+FkbMPMMSLu1wuZex2u51wOExjYyNvvfUWu3fvprKykpKSEux2OxBr8EbebuCPgeHZBxgWiwWbzabCdzHeaDRKY2MjdXV1nD17lpMnT+LxeGJeG4lEiEQiRqHOwB8Fw9gHGBaLBavVqirxFosFs9mM2+3m448/prGxkWg0Sm1tLR0dHZ8I2eNDegMG+grD2AcYJpNJeWUptkUiES5cuEBKSgp33HEH1113HQcOHODMmTMEAoFPvEc0GiUcDg/0pRsY4jCMfYAhBTrpqcPFDeDEiRO4XC5mzJhBQUEBp06d4vz58/j9fvUz0ouPRqMEg0GjKm/gsmAY+wBDD7/NZjPhcJjm5ma8Xi8pKSkUFRVRVFREb28vJ06coKOjQxm6RALhcPgT1XwDBj4PhrEPMMSj+/1+otEoXq+Xo0eP0tDQwK5du1i3bh1Hjhyhs7OTffv28fHHH8eQbMTADWM3cLkwWm8DDLPZrDx6OBzG7XbT0tLCkSNHaG5uxmQy4Xa7cblcnDhxgoaGBmpqakhJSVFhvKQCNpvNMHgDfYZh7FcAFosFp9OJ3++no6MDi8XC8uXLyc/Px+Vy0d3dzcaNG3nrrbc4c+YMTU1NuFwu7HY7oVAIv9+PzWa70rdhYIjBMPYrgHA4TE9PD01NTRw4cAC3201JSQl5eXkkJibicDhITEzE5/NRW1tLXl4eZrOZsrIy1a4zvLqBy4Vh7FcAFosFv9/PoUOH2LBhA+3t7WRkZFBSUkJiYiI9PT1s2bIFj8dDb28v7777LhkZGeTn5+N0OvF4PNhsNjUxZ8BAX2AY+xVANBrF5XIxcuRIrFYrgUCAqqoqzGYzoVCI9PR05s2bx2233UYkEsHhcDB8+HDsdjtms1kZfGJiohHOG+gzTMbxTwOLYDBIIBBQ1fRgMEg0GlWFO6vVqopwPp9PhezSV7fZbNhsNvx+Pw6Hw/DuBvoMw7NfAQhlNhqN4nQ61XirbACBQACz2axCdbPZrJh2kUgEn8+H0+mMIeYYMPB5MFbLAMNms+FwOBRJxmQyYbfbYwgzImxht9vV0IxU8GUWHjAKdAYuC0YYfwWge2kx2HA4rJhy4XAYh8NheG4D/QojjB9gyBCL8OMDgQC9vb0kJiaqaTh91t2Agf6CYewDDMnPpThnMplISkpSRTmInYwzYKC/YMSJAwwxZMnPRYjC7XYTCASUdzeyKwP9DcPYBxhi3JFIBKv1YmBlMpmwWq3q3w2vbuBPAcPYBxgy4mq1WrFarfj9fiKRCAkJCVgsFhXaGzDQ3zBy9gGGtNukz+7xeDhw4ACdnZ2UlpYyatQowGirGeh/GJ59gCFMOfHwHo+H1157jWeeeYYXX3yRw4cPEwgEDBUaA/0Ow7MPMGQm3efz0d7eTmNjI42NjZw8eZL29nai0Sj5+fnk5+d/YrJNV7gxYOByYZBqrgDC4TA7d+7kRz/6EUePHuXs2bOKB5+SksLNN9/MP//zP5OamqposTqzLikpyWjPGbhsGC5igCEKNZFIhPb2dk6dOkVvby/3338///Ef/8HixYvZtWsX3/ve9zh8+LAalLFarTgcDgDa2toMdVkDlw3LP/zDP/zDlb6Iawli7ABdXV2cOnWK7u5u7r33XubNm6cEKrZt24bb7SYlJYXMzEylbCO9eEkHjJDeQF9h5OxXAPoQjB6KW61WRo8eTVZWFn6/n507d+L1enG5XIwaNUpNw7lcLoN0Y+CyYbiFAYaMt54+fZq1a9dy5swZQqEQ9fX1NDQ0AJCXl8cjjzzChAkT2LlzJ7/+9a+pq6sjGo2SnJys3sfI2Q1cDowwfgAhQzDnz5/n/fffV/py0WiUY8eOkZuby3XXXYfFYiE5OZmCggLcbjfbtm2jra2NgoICMjIy1EGQRhhv4HJgGPsAIhqN0tzczJo1a1i5ciX5+fnMnTuXlJQUGhsbSU9PZ/jw4WRlZcUYfE9PDzt27KC9vZ3s7GwlQGkYu4HLgZGzDxBEnGLXrl38+Mc/JiUlhcWLFzN16lRuvPFG2tvb+eCDD8jKyuKpp57CZDLhdDoZMWIEDz30ECaTic2bNxMOh8nOziY7O5ukpCRDlspAn2EY+wBBQvjW1lZOnDjBddddR2lpKXl5eeTn55OZmUlrayuNjY2EQiF1LrvVaqWsrIy/+Iu/wGw289Zbb9HZ2cm//Mu/qPzdgIG+wIgB+xHRaJRAIKCGWwKBAF1dXapl9pvf/IbXX3+dMWPG8MADD1BcXKxeE4lEcDqdMZp0fr9fteoyMzNZuHAhc+bMYevWrfz93/89hw8fxufzqdeHQiF8Ph+9vb1GH97AJ2AYez9BV6CJRCJ4vV68Xi9msxm/38//+3//jyeffBK/388vfvELFi5cSEpKCsFgkG3bttHT08OwYcMoKyujo6MDr9erWnMmkwmHw0FycjIOh4NQKEQoFKK1tZVQKKSkrOTzg8Gg0qkzYEBghPH9BGG6icyzyEsFAgF27tzJRx99RFFRETNmzCAjIwOr1UooFMJisXDTTTdRV1fHxo0b+e///m9uu+02cnJygEuz7gAlJSWsWLGCzs5O3n//fRISErDb7VRXV6sR2UAgQDAYJBgMYrVajZzegILh2fsJfr8fn88XIwEtxv/aa6/x9ttvU11dzde+9jVl7C6XC5vNhtlsJicnh5KSEsxmM42NjXi9XmWo4XBYkWhSUlL4P//n/zB37lx27drFz372M44ePYrH48Hn8+F2u0lMTIyRuTJgAIzWW79BxChCoRDhcFgJU5w6dYp33nmHzs5ObrjhBmbNmkUwGAQuMekAMjIysNlsrF27lj179jBx4kTy8vIwmUxq44hGo/j9fiwWC6WlpXg8Hnbt2sXx48cpKCggJSWFlJQUpTUvB04YMACGZ+83CJtNjDMQCHDkyBF++tOf0tLSwoIFC1i6dCl2ux2Hw4HNZlNhdjQaJTMzk5EjR5Kbm8uFCxdoaGigq6tL6cQHg0HMZjMOhwO/309+fj4LFy7kjjvu4NixY7z66qvU19cr7jxgzMQbiIHh2fsJkUhE5comk4nTp0/zwgsv8Lvf/Y6ZM2dyzz33MHz4cGw2W8zpL6I7ZzabSUxMJCMjg23btnHhwgXy8/OpqKhQnjoajapz2Z1OJxkZGeTl5REKhdi7dy9nz54lLy+P3Nxc5dUNz25AYKyEfoJ4dJPJhNfrpbW1lYMHD9LW1saoUaMYMWIEdrtd/RxcLOqFw2Hl3VNTU5k+fToWi4XDhw9z/vx59fN6oc3pdKrCXWVlJffddx8zZ86krq6O559/nuPHj+P1eo2KvIEYGMbeT5ApNpvNxtmzZ3n77bfp7e1l4cKF1NTUqFl0+Vm4JCstfxcPLpuGnBqjHyrhcDhUwU42guLiYhYsWMDs2bM5cuQIP/rRj6irq4v5LAMGjDC+DxAddyG7QKzBikFK9bu+vp5XXnmFnp4e/vzP/5wpU6aoo5XFi4u3lvBcqvjRaJSuri7OnDlDNBqluLiY7OzsmE0gEAioeXapFaSmppKTk4Pb7Wb//v10dXWRlpZGTk6OGpqRzUMUb/TXG7j6YfTZ+wjJl8VQw+GwarGJEUWjUdrb26mtrcXr9VJZWUlRUZE6Wlk30Pg5dkFmZiaPPPIIu3fvZvPmzdTU1DBy5EhcLpfaUKQyL+8nG1BpaSmLFi3C4XCwbt06/H4/drudESNGqNxdaguBQACHw6FSCwNXP4wwvg/QmWwmk0nRUuXMdNkAAPbt28fPfvYzTCYTjz32GFVVVergB/mZzzIuOdU1Ozsbq9XKmTNnaGpqUn383t5e7HY7drtdbRzRaBSv1wvA8OHDeeCBB7jpppvYuHEj//7v/05nZyc+n0+9t5B93G63UbG/hmCE8X2Afn66tMukdQYXDdTv99PW1kZtbS07duwgLy+PW265hcrKSrUp9LXvbbfbKS4u5uOPP2bt2rVYLBbGjBlDSkoKLpdL8eAB5dnFkMWYhw0bRiAQYNu2bezbt4/KykrS0tIwm810dHRgNptxOp1K387A1Q/D2C8TkmPDxdDe7XYTCoXo7Oxk/fr1vPTSSxQXF3P//fczYcIExWbraytMjyCOHj1KbW0tWVlZVFdXk5qais1mU/JU+rVI1CCDOMnJyRQVFRGJRNi+fTvNzc1kZ2crfr3D4VAbl0GpvTZgGHsfoeflurHL7+vWrePFF1+ku7ubBx98kBkzZpCenq4GVSTk7otnF6acyWSiqamJhoYGUlNTqaysVGOtcgCkRBxyjXCpqp+enk5ubi6hUIjdu3fT0dFBZmYmBQUFyqvLzxu4+mHk7H2EbuxitBaLBZfLhc/nY9euXezdu5e8vDymTp1Kenp6zBHMwWAQn8/3ua0wqfonJCQwbtw4Ro4cydmzZ6mrq6OnpyfGq+ubiKQadrudhIQEFU2MGjWK5cuXM3PmTA4ePMhLL73EoUOHYk6QNXBtwDD2PkDaVHq7DC6SYtxuNxs3bqShoYGqqipmzpxJQkKCMkAp3un99L58XmJiohqUARRlVibqhKkn7Tq4lL8HAoGY+kJRURHLli3j5ptvpra2ll/+8pccOHAAn89nFOiuIRhhfB8gxTC9mi4G5/f7+fnPf86OHTu4/vrr+epXv0pycjLhcDimxSaHPHxeGC+eXY6IamtrU1Nw+fn5lJSUxBQG9c+Q95YWod7mS05OJi8vTxXtmpubycrKIicnx2i/XSMwjL0PkLxbjBxQ5Jba2lpWrlwJwG233caMGTPU8IpUx8Xz9qXqLf18+XNBQQFer5cNGzbg9Xq58cYb1fvGG7nAarWqFEKXnE5LS6O4uJiOjg72799PT0+P4tLrUYdOIDKOmbp6YPRc+gCdkAKXxCPb29v5/ve/z/79+/nGN77BfffdpwxaDmXsa1FOoP98YmIiycnJigV3/vx5Lly4oBh14rmlniAcAJvNpjYZPY2w2WyUl5ezbNkyXC4XGzZsoKWlhX/+538mKSkJl8sVc64cXOThSyphYGjDyNn7AJGWkuKY5N8+n09JQ6WmppKWlgYQUziTv1+OdxTjkve58847efzxx+ns7OTpp5/m2LFjSncuHA7j8/nweDwxYhV6jUE+2+v14vf7KS0tZcmSJcyYMYNDhw7xla98hQsXLqjw32azqX5+V1eXIYJxlcAw9j7AbDZjt9tVMczn87F7925+9KMf0d7ezhNPPMHs2bP75ZQWYcPpG0piYiJ5eXn4fD5OnDgRc0CEcOqdTidWq1VtFEK80TsCMkiTmJhIaWkpX/rSl7jrrrs4cuQIP/zhD9m7d69i2nm9XoLBIA6Hwzgv/iqBkbN/DnTjs1gsBINBjhw5wiuvvMKmTZuYP38+DzzwAFVVVf3SypJ8WSBGarVa6enp4ciRI3g8HoqKikhOTlYMON34dS4AXCICyVisCFampKSQn58PwJYtW1QfPi0tjUgkotIBfQjHwNCFkbP3AdJfh4vU2ePHj7N9+3bMZjP33nsvZWVl/VrIkpqAGJzT6WTkyJHMnDmTt99+m5dffpnp06dTVlb2qcYtM/KSf4vKjT60AxfThcrKSh566CF8Ph9bt25Vm9rYsWMV8cYo0l0dMIy9D7DZbMrbNjc3U1tbi8ViYfLkyUraub9op8Ke06fcdM/sdDpViC4bgRi6GLIo38h0nhi/5PiSk/t8PkKhEKWlpTzxxBMAbN68mWg0yooVK5Tghj4/b2Dowgjj+wChrppMJt577z2ef/55MjIyeOyxxygpKVGSzv1hDDLQYrPZVEVf/l3Ocz958iSFhYUUFxeTmpoaE2br7TjZBOR0GYlQ9GhAyDd2u52ioiJCoRCbNm3i7NmzZGdnk5WVpcg5hrEPbRie/XMgxhcMBmlsbKS+vh6fz0dxcTF5eXlKr70/Ie+nM++i0SiVlZUsW7aMXbt2sW7dOkaMGKF47jp9Vph0+mScbAS6JJbk+5IuVFVVMX/+fPx+P1u3buX111/HYrFQXV1tTMZdBbjmv8F4Cmv838VI3G4369at480332T48OEsWLCAnJwcJTelD6R8UejsO7PZrFpiKSkpDB8+nLy8PI4dO8apU6fw+XwkJSWpawBiNOPl9bqWPVxMTaRQJ/cgmnYPP/wwDoeDDz74gEgkwte+9jUqKio+kbvHy2v1F/QIRN5f/0z9/wz0Hdd8GC/tLbjoSUWUQqrwYhQ9PT28//77rF+/nnHjxvGlL32JwsLCGOpqfy7AeLFI8c4Wi4WKigrq6+upra3F6XQyadIk4KK3lsKcDN2IkeveXY8A9LBfWoyZmZlkZGQoias9e/Zw0003YbVaVe4eCoUU96C/9ekDgQDd3d0xqZH8rhccjbTi8nBNb48yNCILXS+GySJ2u910d3ezZs0aNmzYwOTJk5k3bx6pqalqU+hPyWZdaioQCCijl0EYp9PJlClTyMzM5MKFCzQ3N6vz5YRN19vbqxhzgGLEiaHoPfN4qaxQKKRae/PmzeOWW27hxIkTPP3009TV1cUU/OT9u7q61MEXXxT6UI/H46Gjo4Pu7m56e3tpa2ujs7NTSXYbYpqXh2s+jJfiloSHVqtVTazZbDZ8Ph+rVq1i5cqVuFwu7r//fm655RacTidATFurP8J4ORRSn64TdVm5XqfTyaxZs+jo6ODDDz/k7bff5qabbiI1NRW4dD6ceGKBtPTioxBR0ZHPikQiJCYmMnr0aKXC8+qrr5KQkMA999xDTU0NycnJKg2QzVGewxfFuXPnWL16NV6vV22merswLy+P22+/naysrC/8WdcSrmljF/aZzi0XDyUVbIvFwm9/+1sOHTrEI488wpw5c5ShwyXj6C/PLqQaOT7q+PHjnDhxguzsbKqrq7Hb7UQiEebOnUtdXR2vvPIKCQkJ1NTUKLquy+WKOdxRjEUn6+jeXdeuF48thcGKigqWL19OT08P27Ztw+fz8dBDDzF+/Hh8Ph/hcJjExMTLGuH9PLjdbnbv3s27776Lw+FgxIgR5Obm4nK5aGlpwWazcd111xnGfpm4po1dvLleaJIFLGOqDQ0NuN1u0tPT1Tio7smEotpfxm42m0lISCAcDtPe3s4rr7zCL3/5S2688UYee+wx8vPzaWlpweFw0N3dTTgcpru7m4aGBuUJZSIPLlX2hQtQXFysGHIC6cfrkY0IXJpMJkpKSvi7v/s7vve977FhwwZsNhspKSlkZ2eTkpKiNon+eAYmk4nRo0fzgx/8gJ07dxIOh1m0aBFLliwBYMOGDezdu1dtLkbe3ndc88Yuhy9IiJuUlKRUZc6cOcN3v/tdmpubeeCBB5gzZ47KbcVjyqmp+iEQX/Sa/H6/Kq7l5eWRmZnJjh07OHLkSMzxUS0tLQQCAXbs2MHRo0fVdUi9QSIViVxGjhzJN77xDaZOnao2AdnofD6f4v7LM5ENz+/3k5qayle/+lVSUlJYv349Ho+HRx99lDFjxuB0OlUHoT8MXr4LKZ52dXXR1NSEzWZj8uTJTJgwgfT09C/8Odcarnlj/7QBD7PZjNfr5fjx43R0dJCVlUVhYaEKj0WsES6GzEC/hvL6e8+aNYve3l7Wrl1Lb28v0WiU5ORk/H4/2dnZOBwOmpubY1p/0juXFEPuUwp5+v3L78KB13XtZBOU6KWkpIRFixZhsVj44IMPeOWVV1i0aBHjx4/H4XD0m5fVD7IIBoO0tLSwevVqotEoX/7yl8nLyzOq8X8ErmljF0/k9/sJh8PqdFWfz0dtbS0vvPACgUCA++67j6lTpypqqhTv4KJhSZtLz+X/WMgCFy25YcOGsWDBAiZNmqROgtHFLTZv3szLL79MRUUFixYtory8PIZCKz8nYhqlpaUqepBnIMYuxhN/Fp14fLvdzqhRo3A6nVgsFjZu3EgwGCQpKYnKykpcLle/FOgkPTKZTHg8HsXZHzlypCqIGpX4y8c1beyA8lxSTY9EIuzatYtf/epX1NbW8pWvfIV58+ZRVFSkFGh0Y+vs7MRut/cboUZ66eJdExMTqaioiDnVRULuSCTCsGHD8Pv9fPTRR3R2dlJdXa0IMPGnxkgfHmJZdeL1JTXRaxiyUUhdwmazUVFRwX333Uc0GuWDDz7g5z//uSLeiJF+EUi/X9qHhYWFACrCMDz6H4drus8Ol+iw4pUikQjHjh1j+/bt2O127rrrLvLz82OOb9JVaPRZ8v6AtNbk84S3LhsSXAzvJeyurKzk5ptvpquri+3bt9Pa2qpaYDoH3mq1qtNfAcW9l1/6/ckv+WydySb3XFlZyfz585k2bRqHDh3ipz/9KUeOHIkZxpGNUYp/+kb5WdAHfRITE5kyZQorVqxgzpw5SkrbCOMvH9e0Z5fFK6Gh3++ntraW/fv3k5aWxu23305qamoMQyz+CKeUlJR+H2/V6aCRSIT6+noOHDigCndixEKWOXToEG1tbQSDQd58803q6+tjPLp4+IyMDCZOnEhRUdEnPku/B/1exMtKTUKPBIYNG8bcuXNJSEhg3bp1OJ1OFi9ezPjx4z8RauvTeJ93/3qbUDa/SZMmYbFYcDgcRhX+j8Q1b+xCLRV1lg8++ICNGzcycuRIHn/8cWXM+mt0/Ck42npl22KxsHPnTv7pn/6Jjo4OtdlIbxxQFN/Ozk5++tOfqmuS38Wr1tTU8PTTT1NcXAzEcun/kPHEbwBms1l1K5xOJzU1NSQmJtLT06OOqU5MTGTEiBExG4g+dvt56Orq4sMPP8Tv9xMKhWhsbKStrY3i4mLFAjQUcS8f17Sxy2J3Op14PB68Xq8aDElLS1MDJgMJCd11jyzXE1+UEoZcKBTC6/XidruxWCykpKSolESvuCclJamc+nJovsIrkLxdrkk4B1VVVXzta1+jpaWFN998E7/fzzPPPENiYqKqZwhRqC8GevToUb73ve+RkZGBzWbjvffeo6CggEcffVQNJcWP9Br4fJii13BZMxgM0tvbi9PppKuri2effZZf/epX3HnnnTzxxBOMGjUqJj8fSOi5bXt7O21tbcAnPa2E87t27eL555/nwoULPPnkk4wdO5akpCTVIZC8PTs7W21i+sjrZ0HCdj00l2KlrlXX2trKf//3f7Ny5UomTZrEd7/7XQoLC1UnQDaLz9pgotEoPT09nDt3TqVXoVCI9PR0CgsL1eYm3QHj6Kq+45r27JIPBoNB2traaG5uJhwOk52dTXp6umKhDXQFWM/LRbVGpK/EQ+qjrxaLhaSkJDweD7/85S957bXXKCkpYfz48TGVfWnr6a3DvuS/sikIlVh06SORCE6nU8375+Xlcffdd+P1ennvvff4yU9+wtKlSxkxYgRdXV309PQoaew/tIGaTCYSExMpKytTf5f8XWoUkUikX/v61wquaWOXxXL+/HnWrl3LsWPHmDZtGjfccANJSUlXRJ1FF5zUJ9Kk2q97RinAmUwmcnJyqKmpITU1lb1793Lq1Cn8fr+6D71Yp1fp++rd9dFYQF2jnkpYLBaGDx/O4sWLMZlMbNu2DavVyl133UVdXR2HDx9mxowZ3H333Z/7mcJ70IuoxmjrF8M1Pc8eCoU4f/48K1eu5Le//S05OTmsWLGCG2+8kZSUFKXE2l+8775CN0R9Gk08unhnfWJP8nC3283x48cJBAJkZmYybNgwVcGWop4+5dcXiqs+8ivGLQU3iRbk2qxWKxkZGRQXF9PT08OuXbuoq6vj/fffZ/v27QwbNozp06d/5kYq1yrRg9x/NBpVLVL9Mw30Ddf0k4pGo3R1dfHuu+/S1NTEzJkzmT59uspp5RDFgUZf8lqdBiuGX1hYyJw5cygtLWXTpk3s2rVLGYm8TqBHDX2BGKBEEvF9fPHu0knIzc3lpptuIhqN8s4773DixAmqq6sZPXr0J67l0+5fpg7hYn1Acn79ZwxcHq7aMF7v6+rFLPFmJpOJ7u5utm3bRm9vLzU1NYwcOVIVtIRxlpSUNOALK74Ip4fwAA6HQxXN5DRXMcCsrCxmzpxJc3Mzhw4dora2lilTpsSIUgrkeej9b31UVb8Oh8OhFH2khiGhvM1mU1OAkUiEc+fOsXv3burr6zl//rwq7omApWwMcl/6hqUr/+hhvC6pJc/ACOcvD1e1sUuoJwtGvJOExy0tLfzyl7/E4/GwePFiqqurY4QSdCHHgcKnEVs+rbcveawwAAWpqaksXbqU3bt3s2XLFkpLS5kwYYL6f70lJxufrnIjv8vP6p8ZD3kfCacbGhq4cOECu3fv5te//jXRaJSMjAzy8vKwWCycPXuWt956i8zMTCorK2OIQ1L8k2m/T3vuOgXYMPTLx1Vr7HBJbDEcDivKqVSw/X4/ra2tNDU1kZubS3JyssqHpXotRjQYGVuyYYm3CwaDSg8+JyeHxMREuru7aWlpUfrwSUlJapMAYnJeXaNeV8XRxTR0cU1AVeG7u7sJBoM8++yzrF+/XslpjRkzhm984zN4deAAACAASURBVBuMGzeOYDDIT37yE9asWcOFCxf4v//3/6pnLNfR09NDIBBQ9ZI/dN8G/jhctcYus+YyoipMOfEYGzdu5KmnnsLpdPLoo49yxx13kJqaGtOSEsN3OByDsp+rV8L1o6QBcnJy1ABJW1sbubm5BINBurq6SEhIUIdQuN1uNa8u4bmEzHp+LpuJ/lxCoRC1tbX85Cc/obGxkZMnT2IymbjzzjtZvnw5TqeT0tJSxfV/5JFHsFqtvPnmm3z729/mW9/6FsOHD8dms9Hd3a0mB/UQ30D/4ap9olKxTktL+4Suejgcpq2tjZMnT5KXl0dpaSmZmZnKI8nRxaLNNli9iZ7PyjXKZNuMGTM4efIkO3fu5LnnnuOb3/ymOlBCTrjRx3rFuKS9Jb10SXt0DftIJMLu3bv5zW9+w7Fjxzhw4ABut5tHH32UmpoaiouLmTJlikoJ5DXFxcV8+ctfxmKx8OKLL+J0OvnKV75CeXm5ui6p+Bvof1y1T9VsNuNyuWIUVi0WC4FAgG3btvHOO++oxSeLTRa0zk0frARD8brxBSwh2UyYMIEtW7awfv16du7cSXd3NykpKTH9dtGbi0Qi+Hw+xTePb8uJN29tbWXr1q0cPHiQI0eOsHPnTtLS0rj33nvJyclhzpw55Ofnq4Kf/C4bLKD68B6Phx07dvDSSy+xYMECxo8fH3Om/GBMnYY6rlpj11tDUg22WCwcOHCAF154gQMHDrBkyRIefvhhlcuK6ozktEIJHYwGr6vE6iG3GFdmZiZTp05l165dNDU1sWnTJmbOnElmZqbqtYtBSl1D5+NLXUMEM9auXUtjYyNvvfUW27dvp6ioiGnTpjF27FiWLl1KYWFhDNHGZDLFHE6hR0pjxozhq1/9KpFIhC1btmA2m0lLS6OysvITirgG+g9XrbHrBiBFpmg0yqpVq1i/fr0ScBTNNlmUcKnyHF/pHkyIHx8Vw5K8GuCWW27h/PnzfPe73+X555+ntLSUwsJCNZgieX4oFCIxMVHRUSWEb2hooLa2llAoxNNPP43b7WbYsGHMnDmTqVOnsnz5cjIyMlQrMBAIqPl3fSpPb4PK5lRYWMjXv/51bDYbmzZtwuv1smLFCkaNGmWE8X8iXLVPNb43293dzalTp2hoaCAtLY3Ro0crTTnJ6ePbOvGz5YMJ+viqzoLT2WdwsWIuJ83K/39aeC19cpPJxKlTp2hsbGTbtm289dZbysiTk5OZO3cuN954I0lJSWRlZaminuTcutad/kx1cg9c7M0XFBSwbNkyLBYL77//Pi6XiyVLljBixAiSk5ONML6fcVUbO1zSde/q6uLFF19k37593HTTTdx9991qTBMuLnb9THNdgnmwSiGJ8eg9aV0w0m63q2mxYDDIuXPn6OrqUjP6ktrYbDba2tpoa2ujpaWFNWvWsHv3bpXC5Ofn8+STT5Kbm0tBQQFZWVmfmFWX69AlqaUu8Glju/J/w4cPZ+nSpQQCAfbt24fFYmHp0qXU1NTEkKJk442/XwN9x1Vr7OLBZIG1t7fz0UcfEQwGKS8vp7i4OEZOWZdfEq8ni3QwLiwpIsIl766TYcRAampqePjhh3n22Wd58803KS8vZ+LEiTERQHt7OydPnuTll1/m8OHDtLa24vF4mDZtGvPmzSM7O5sJEyaowyDioSvdiJHHR0p6JV/fBOT02CVLluBwODh48CDBYJBvfvObpKSkqFNyhXgj39Vg/V4GM65KY5fiks/nw+Vy0dzczOuvv059fT2LFi1izpw5JCYmxoTAfyhUH4z9dUClKOJJhSwjM96hUEhx1IcPH040GuX06dN0dnYqY4tEIhw8eJAf/vCH+Hw+Dhw4QDQaZdGiRdxxxx0UFRVRWlqqRC/+0DPSjU7/mXgW4KexAkVqa9SoUcqI169fT0tLC88884xKsSRN8Pl89PT0fCbxxsCn46p8WpKvy+I4d+4chw4dwuv1Mnr06Jiq71D1Dh6PRxlAfFgrXl8KlHKE07vvvssbb7xBRkYGTU1N7Ny5k5MnT7Jnzx4cDgf33HMPo0aNYvz48ZSXl2Oz2XA4HIpB1x8Qz66Tl0Q1tqqqijlz5hAKhfj973/Pf/zHf3DPPfdQXV1NQkICoVBIFRCFDzAY6ymDFVelscMl7fFz586xYcMGuru7ueOOO6iurlbDLkPV0PVBFZ3tpuvTyb1ZLBYKCgqYNWsW77//PqtXryYcDtPU1MSePXvIy8tj2bJlJCQksHDhQsrKyj5BmRUlmv6Czs2XzUquf8SIESxYsIBAIMDq1asJBALcf//9jBkzRtVVdD6Agb7jqjX2YDBIc3Mz7777LuvWraOoqIhvfOMbjB8/PqYHPBQN3mQyqWOqpJou0k86aUburaWlhT179tDe3k5nZydvvPEGI0eO5IYbbuDP/uzP+M53vhNDKpIRUz3X7s9r1/n5slmJzLTVamX06NF8/etfp6OjQ0l6L126VE0lSk1gKH53VxJXrbED1NfX8+yzz5KVlcVDDz3E5MmTMZlM6qzygRal6E8I6w2IOUVV9/KdnZ00Nzeza9cu/u3f/o3u7m7FJ1iyZAlLlizB6XQqPXn9tBUxPBmA6S/Dkoq91FNkvFWGePx+P8FgkGHDhvFP//RPPP300/zud78D4K/+6q/UnIK0Cg30HVelsUciETo7Ozlz5gwWi4Xs7GwSExMB1LFHMpwxVKETgeTkWafTSW9vL/v27cNms7Fx40ZWrVqF3+8nKyuL5ORkWltbVfFSlGhlA9Q58roKrZBl+sPgxSvL9xF/jLRU6E0mEykpKTz22GOkpaUp4s2DDz5IdXX1kI3KriSuOmMXz7Zv3z5eeOEFMjMz+dKXvkRpaSmAIn6IZx+KCyaeOy5nuZ89e5YzZ87wwgsv0NzcTE9PD263m/Lycu699156e3tZtWoVe/fupbe3V/XcpdIuxh3vMXXD7ws+65lKu0/4DVJ3ANRhjlI8tdvtVFVVcc899xAKhdi0aZPS1KusrFSnwxjoG4aksesLPX4BRqMXddhOnDjBoUOHmDZtGjU1NaSnpysDFzroQOftn2cs+nXoRbhPe53NZsPtdqve88GDB1m9ejVnz56lvr6e3t5ebr31VmbNmkVaWho33HADPp+PzMxMuru7Wb9+PRUVFSxevFh5dX2GQHL/SCSiKue9vb3q8/7QdTudTjVj8GnQ+fjxaZQ+aSefabPZGDVqFPfffz82m429e/cSDod5+OGHGT58+GcKWQzFjfxPiSFr7OKBZHHo8srvv/8+a9eupaioiHnz5jFs2LCYiSpZ0LqSzUBAIgq97Rdv1JIzS04qzDMpaIlRAmpybNOmTZw6dYo9e/Zgs9mYP38+xcXFTJw4kYkTJ6pR1oSEBCZNmkR+fj6rVq1SZ7PJwRjybMUQ5Zrluf3mN7/h0KFDMc9R2nNyesusWbO47bbbYmYT9ChKwnR9ak+eQbxEtmwEVquV6upqlixZQjAY5ODBg/ziF7/giSeeICcnR9UWdKqu9OwNXMKQfhp+vx+/3x8z3hmJRNizZw979+5lypQpTJ06VU21xffWr1SBRyi8srDFAODSPLlAr6zrhyWuXr2a+vp69u/fz8aNGykrK2PevHmUl5dz2223UVRUhMvlipkiM5lMJCcnM2fOHFpaWjh06BCrV69m8eLFn5CZ/jREo1F27txJfX09VVVV3HjjjbhcLhISEgDYvn07GRkZTJ06VSnaytCNfk/xHl3fbGVT0KmyorVXUlLCggULSEhIYP369ZhMJpYtW8bIkSNjmHqRSITe3l4SEhIG7SDTlcCQNPb4yrN8yT6fj/3793P48GHy8/OZPn06qampn0vZHCjIVJmukqpfExBzbfIa+f/GxkZ2796N1+vljTfe4Pjx4+Tl5TF//nxGjBjB7Nmzyc7OJjk5WVWtdT45XAyzb7/9dmpra3njjTdYu3YtCxYsUM8RLglc6kZqMpmYPn06mzdv5uDBg5SUlLBo0SKys7Ox2+14vV5SUlIoKipSn6l7c+kQ9PV56xuORG8JCQmMHj1afdfr16/H6XQyd+5cRo8eTWJiooqeJE2TcV4DQ9TYdaFDh8NBMBjE7/dTX1/Pz3/+c86ePcudd97JokWLyM3NVaG6vhBMJtOAK5SGQiF1trp4XDF8fQxUwl7Z0Jqamjh16hS7du3iueeeo7u7m6qqKkaMGMEtt9zCAw88EJOayMiprq0u9xkIBHA6nVRVVZGZmUlTUxMHDx6kpqbmE2fb6YKQFouFtLQ0UlJScDqdJCYmkp6eTmJiIi0tLeTl5bFw4UJcLldM4Uyfeutrb1xPJSTacDgc6thqmVjs6enhrbfeoru7mxUrVjBy5EgCgYCaZNQ3GQND8JAI4b0Lp1oWwdmzZ3niiSfYsmULf/7nf863vvUtMjMzY8QddA14CesHEnJGuhSp/H5/DAtOwnvJaT0eD93d3bz++us89dRTrF+/Hr/fj9ls5h//8R958sknmTJlijpA0eFwqNBdl5MSQwsGg/T09GA2mxk3bhxut5u1a9fy0UcfMW3aNNLT02PUeMVIZYPq7Oxkx44d1NbWkp6eztixYzl+/Dj//u//TnV1NZWVlWrmIH6GXZ755ZBh9HxfxELdbjeRSIS8vDyuv/569u/fz/r163G73YwfP55oNKoq9rI5GIW6ixhynl08snz50jf3er0EAgFSU1NJTk4mFArh8XiIRCLqFBFZePFSygOJcDis8kmn0xmTk4uX7+np4ezZs/zqV79i7dq19Pb24vF4mDx5Mk8++ST5+fkUFhaSnJys8nir1arOpnM4HEqUQ4ZjZBNJS0vD6/Xi9XrVBtPa2hojLBGvPqvr1Hs8HsLhMIcPH+Y73/mOkrOSWoK0z4THEF+E68szl03K6/Uqg5WiXXJyMuFwGL/fT1paGk899RQ/+9nPWLVqFb29vXz3u98lNTVVPQ9p4RkYgsYOl7x7MBgkISGBw4cP81//9V+cO3eO5cuXM2vWLCUaqee/uscCYqrEAwHJI10uF9FoNGYxNzc3097ejtls5sc//jHnz5/n9OnTdHd3c8MNNzB79mzKysoYN26cysclnxfCi+5BpY2m98/lvDRpNyYlJZGSkoLdbqe1tZXc3FzlFfUiIqAiAkkzysrKmD17Nm1tbdTV1annKoYVX/yUkFp/z8+DTv/VZbcAVYEvKSnhy1/+Mmazma1bt/Kzn/2MxYsXU1NTo56tgYsYksauj6WGQiHOnDnDjh07iEajTJ48mcrKyhh5JimMiYeDK1OJl0UrnhIu5tC9vb3s2LGDDz74gFAoxLp164hGo0yfPp2xY8cybtw4rr/+ehXR6PrunxYa63Pk+t91sYpQKERNTQ133nkna9asYc2aNaSkpDB8+PCY8+CklSX/JhuHnDxjs9k4dOgQeXl5MWq8Ovdd73705blLvUGGZOQ+ZRPTP8dms8Uw6kTTLiEhgdLSUhXVGRiixg4oD9LQ0MCmTZsIBAIsWLCAioqKmGq9/mdALZwrkcuJUXo8HnXAwvr166mrq2Pfvn1s374dp9PJokWLyM/P56abbmLMmDGqny3Xr+fk0pOPP/BBl6mCS6GxGEk4HKampobOzk5efvll1q5dy4wZM6ioqIhR7ZFNIjExEa/XC1zatOx2OyUlJZSVlan2mM4N0OslcImJ11fop9nG9/31LowMzzz88MNEo1F2795NOBzmoYceUrP8Rt4+CI09/osUyJ/lyKNIJMLJkyd5/fXX2b59O5MnT+axxx6joKBAGYRO4viixi0LTzci/TCD+NxUv2YhwcjPNDc3c/jwYc6ePcvKlSv58MMPKS0t5dZbbyUnJ4evf/3r5ObmKiEK/dnIZqX3xHWj0Dc2/Vp1o9frHsXFxcyePZtdu3bx4YcfMmzYMAoKCtTr5fPFU3/a5inFxq6uLpKTk2O06WRj0b3z530P8l3pY7b6/5nNZlWf0EP7qqoqli1bRigUYtu2baSmpnLPPfdQXl6u1kF88fBaKuANKmOXxSwLWSd46NVqCTHr6upYuXIlhYWFLF26lOLiYvVzwlSLX2B6Xns51yWfrXsp3Yj165VfspCkc9DW1saePXs4ffo0q1at4ty5cxQWFnLrrbdy/fXXM2vWLJKTk8nLy4spKunhuBiRTvONv0+JAuT/9U1I/zeT6aKwxYoVK9i3bx9vvvkmFRUVlJWVqfFZaU8GAgH279/PqVOnMJlMXLhwgQ8++ICMjAx12m1SUhIjR44kLS1NPR9pM8afWPN50KOZ+Ou3WCyKtCPRh3w3w4YNY/78+SQmJrJx40aCwSB33303I0eOjGklSvFODsm4Fgx+UBk7XCqaxRdmdKniSCRCU1MTR48eJRgMUlhYSEFBgepd67x3wRf9MvXRTLg4VioLWh8U0ckxcu2hUIjm5mbee+89fvWrX6nNobS0lEWLFjFlyhTS0tLIzMxUHvfTrlfftD4t6vmse/1D/+ZyuSgtLWXUqFEcOXKEw4cPxzDgpPhntVo5ePAg0WiUKVOmkJSUxNatW9XpMmazmenTp8dce3zH43K/gz90j/L84oUuhUMwduxYnE4nXq+XTZs2EQqFuO+++1QOLxuEfJfXCvFmUBl7vMfSjUe4ztIrXr16Nb/+9a8ZN24cy5YtY9iwYVitVrq7u7Farf3ebpEwNCUlRV2bfoBE/CYTjUbxeDxqdn716tU8//zzhMNhsrKyePLJJ5kwYYJ6P6ku+3y+Pyjs+KeA2WwmLy+Pb33rW/zN3/wNr732GgUFBSxcuFDNE8hgyuLFi/nSl75EJBLB6/WqFp8IZ1gsFlJTU9Xr9IKeHvr3B6S7ILUKIVnZ7XacTqeSsvL7/axZs4b29nb++q//moKCAsxmMx6PJ6atdy2IYQwqYwdUyAiXxlH1EM7v9+P1emlra6O1tRW73a4OKpBQur9FKXQPJSw1fWLO7Xar0FJ6zn6/n7a2Nv7zP/+TgwcP0tjYSFlZGX/913+N3W6noqKCtLQ0gJh2VH8aRF8gKY8MlHR0dNDT06OKecI69Hg85Ofnq2hGV8aRE2Uk9I5PnfTvsD+hh/B6YdDn8xEIBCgpKeEv/uIvMJvNvPPOO0SjUb797W+TlZWF3W5X1f5rJW8fVMYunlxf+DpzSvKsdevWsW7dOkaMGMFdd91Ffn4+ZvPFU1pleisQCPSbbppch/TGde8tlXDxNHa7nSNHjvDrX/+aY8eOsW/fPi5cuMDtt9/O1772NaZMmRLTI9c9nsViUTTPgYIYiXhiMQB99kAq70J0iUajMSfIxItexrfdZJPszw1Y3lN3DIAiD0mYX1lZyYMPPojD4WDlypU4HA4efvhhRo8erVqQ8TJeVysGlbHDJS8nVVy9+GUymeju7mbfvn0cOXKEOXPmMHXqVNLS0lR+rPfS+/Oa5DqkpqAbbDAYJBAIUF9fz9atWzlz5gxbtmzB7/czY8YM8vLymDZtGtdff71ahOJR4je4K7HgzGYzqampzJ49m9///vesW7eOkpISpk2bRkJCggp3pSAm6QpcGtQRj67XKgSS8/f3vclGIs9O0ipRq/V6vVgsFqqrq7n33nvx+Xzs3buX5ORkFi1apNqaV7uRCwadsetfoPRuJRfz+/3s3r2bpqYmhg8fztSpUxX/3e/3f0JSqb+gk1L0k01kM9q9ezenT59my5YtvPrqqxQWFjJu3DgqKytZvny56v3Le0jUEV8Uij9ccaAQjUZJT09n7ty5fPjhh7zyyitUVFQwbtw4nE6nKtIJ0UXyXKkz6GG8GE98KK/n7v1xb1IzES+u6+fLd6MPAY0ZM4ZvfvObPPvss7zzzjsEg0FWrFhBaWnpNTP3PqjuUkKz+AXi9XrxeDwcOHCAV155hWg0yuOPP868efNiDnuQIlr8pFd/XJdci+Sr3d3d1NfX4/V6+c///E8OHDhAamoqt956K5MmTWLBggXk5+fjdDpVuKgrwehcAvGIEpkMNMQzJiQkUFlZSWlpKa2trRw/fhyHw0FGRgZwUT9AxCp00o1+lpzuacXo9Bn1/vxOdH6BHgGGw2HlJAQWi4Xi4mIee+wxIpEImzZtwul0snjxYsrLywe0KHqlMKiMXRaHztxyOp14PB5Onz7NSy+9xKFDh1i2bBm33Xab0n+3WCxKCkn3ILogg3yROjnmD3kZvY2mL6BQKERbWxvnzp3j4MGDvPzyy7S3t5OYmMjo0aO5/vrrWbp0KWlpaWRkZHxiGEPnCejhr9y7zuMfSMhnp6WlMWfOHI4cOcKGDRvIysqisrJSeXWhnuoFN3ltMBiModTqrVN5hv1NUZZNRp+Mk2cq+bxci2wIpaWlPPjgg9hsNt59913MZjOLFi1ixIgRKnKT+9LTt6thIxhUxg6xhwQK/H4/jY2N1NXVkZqaSnl5OVlZWTEFIB26sYs3BVQlHfjEwYPxpA+pqDudTgKBAOfOnaOtrY29e/eyZs0aOjs78Xq9uFwuli9fzrhx48jNzaWkpCRmcegLXTaR+AUoEc1AV+L1+5UQPScnhxEjRrBz507OnDlDY2Mj2dnZ6lnor9GNXsJp/d5144f+nUeQ56YzGPV/l4hDDFbfhKqqqpg7dy4Wi4V9+/YRjUa55557VB9e7k309j6L+zCUMOiMXf+yxGBPnjzJSy+9xLlz5/i7v/s7brjhhs+s7uqvl3ze5/OpM8t0FRO41O6KJ2lI+nD+/HnWrl3Ltm3baGxspKmpiaqqKh588EFKSkqoqKggPz//U4UW9Wv8rMX+aZvWQCCeWutwOPhf/+t/0drayoYNG/jNb35DVVUVLpdLRUV6/1znv+shvNzTnxqftQbiU0IAn8+H1WqlpqaG5ORkXn31VbZs2UJvby9/9Vd/pTYJ2Xyl+yJrZyhjUF29vlNLvzQcDnPhwgU+/PBDvF4vY8aMoaioqE8LSSeESJgn7617U316TEgwJpOJzs5O/uVf/oXm5mZOnDjBhQsXuOGGG3j00UcpKipiwoQJpKWlXbHwuz8ghiqeKyEhgVGjRlFcXMyFCxc4cuQIPp+PaDSq6g/xHQSZYx+ME2a6iIdAiDdjxoxR+nsbN27E7/fz+OOPU15ejsPhUP16p9OpnMNQ9u6DytgF0ju1Wq3s27eP//mf/8FqtfKXf/mXiv/+eQ9dD+WF3633f0UJRtcvlxbavn372LJlC+fOnWPNmjUATJs2jQkTJlBTU8OkSZOUWqtUpocq9JRC6gv6opZUSBRwpBAqvPn4yvdgg15bkB68fg9VVVUsWrQIk8nE//zP/+BwOLj//vupqKhQqruSogx1DCpjj0ajSpJYCi3Hjh1j48aNOJ1O7r//fvLy8vq8u8qOLgtWvmy4xF0XIozf72fbtm3U19ezZ88e1q9fTzQaZfbs2WRmZnL77bczadIkbDZbzDloQx2yiIPBYEy1fMyYMUydOpXz58+zatUq7r33XiV+oXPJr0Sd4XIgm7HObdDbdA6Hg7Fjx2Kz2ejp6eHdd9/FbrezcOFCRo8eHZP3D3UMOmOXcMnn8/Hxxx+r9s/48eMV77ovu6xeONLpnfEerKenhxMnTnD69GleffVVNmzYQF5eHqNHj6agoIDvf//7JCcnq1RATwH0AuBgC1/7CrkH/Wx3k8nEjTfeSGNjI//6r//Kj3/8Y+644w5SU1OxWCwkJSWpARh5jvqcwGCCPuMvHAlhBLpcLrxeL5FIhJqaGp566in+9//+37z33ntYLBePxiorK4sp4A5lDCpjN5lM6rA/j8fDa6+9xhtvvMF1113HD37wAzIzM5WAwucZl3C6bTZbzDy7eCaPx8O5c+doaWnh7//+79m3bx8ZGRkUFhayZMkSHnnkEZKTk1XVXufc64va7XargZChaPBCedVDcrlHp9NJSkoKXV1dfPzxx0yaNInU1FTgUiQgHPOBVurtK/QBmXjRUdmo5Fdubi7PPPMMzzzzDK+++io+n4+vf/3rFBQUXBVjsINKXTYajdLV1UVHRwevvfYaL774ohKlkBlrmY/+PO8uObs+/ghw7tw5Tp8+zcaNG/nHf/xH1q5dSyAQYPTo0Tz66KN85Stf4brrriM7OxubzaaIJLqHECFHCQmFSTYUF4Pe3w+FQur5dHR0KI+/e/duDh48SHJyMtFolNbWVlpaWujo6MDtdsfUPQZbbhsIBGIo2LImAKUzoLc9XS4XJSUluN1utm3bRltbG3l5eerAiaH4HQsG3LN/HmVSxBfr6uro6uqiuLiY4uLimLPI9NfGv1c8M00qxR0dHQQCAV5//XV27NhBV1cXra2tpKam8uUvf5nx48dTVVVFbm6uCk9F+lnvz8sOL4tEIpHLEVIcTDCbzcpYu7q6WLlyJRs2bMBsvig93draSk9PDx9++CHPPfccGRkZ6hlbrVZGjhzJfffdR2Vl5aC8f73VGi9AKROKejfCZDIxYsQI7rvvPiKRCJs3b8bhcCjiTbyH1ycyB/tGMGDGrveyRatML5bI371eL++99x4HDhzguuuuY8aMGaSlpSl2k07F1DcO+SVnpFksFvx+P52dnapPfvToUT766COam5sZO3Ysf/u3f0tqaioTJ04kJycnhgAj7yuz2dK20/v7krtLe2coQq+6e71eTp48yf79+4FLXH2Hw4HH46G+vl4tdl2UUqKcwfgMdE5AvEHqhCqdMyDz8IsXL8ZsNnPgwAHC4TArVqwgMzNTCWBIqiidicH6DAQDZuzxRx9Ju0qfkvL5fHR2dnLw4EHa2tqYM2cOo0ePJiEhQYWU8qAFergOqEMUotEoR48eZd26dTQ0NLB161bOnj3L7bffzvz58xk9ejSzZs0iMTHxE7l2vIfS+//ydx1DMVcX6EXGxMREbr75ZjXbHggEVGQkwhvTp09n0qRJwMXnUFhYqDbKwYrPujZ9sEnvTJhMJsaOHYvdbue3hTTICQAAGnJJREFUv/0tW7ZsIRwO8+ijj5KXl/cJjT2Px6MmBAcrBuzK5KEI7VLOFAdiwsj33nuPM2fOcN1113HjjTeq450kfJeCWPzIpXh0gK1bt7Jnzx4+/vhjtm3bhsViYfLkydx1113cdtttTJgwQRFABvNOPBDQoyLZeEWuSXrR4rl6e3vVpqszEPVTY3QpsKECXVNAr7wnJSVRXV2tujdr167Fbrdz9913M3z4cDXTL6QsWaeDdeMbMGMXFRMpiujGDhcLKXJY34ULF5g7dy5TpkxRVVQ5101OJNEFFkKhEJ2dnezdu5eOjg7eeecdpS46duxYKioqmD17NkVFRaSnpyspqKEcfvcXdKqr2+1m586d/O53v4thFepTZPv27aO+vl59h5MnT2bixImkp6df6Vv5oyHPQByILrlttVoZNWqUijx///vfEwgEWLhwodoIAFW8G4ztR8GAenabzRZz4ojT6VTG2tPTw+HDh+nq6qKwsJCysjISEhKUMcrP6dNtFouF9vZ2Tp48yenTp3n22Wc5fvw4GRkZlJaWMnbsWFasWEFOTo5qo+l5mq5Ae61Coq2EhAQ1zionsYrun/SiW1pa6O7uxmw2U1BQoHrRNpvtE+nVUII+/ASX0jIhETkcDsaNG0d6ejrt7e288847wMUTcQsLC9WY9WCfjjNFB2griqct9vT0qP5nMBjk+PHj3HfffSQlJfHAAw8wf/58MjIyFJNOXiNjjZJnvv/++/zrv/4rDQ0N6jO+/e1v8/DDD2OxWEhISFCVcn1WXC+yDeYv6E8N8do6hdjj8cSw5CSSeuyxx6irq2P+/PksX76c9PR0HA4HiYmJSgJsKD5LcSRut1vNtUvUJ7ULv9+Pw+Ggq6uLJ598km3btrFo0SKeeuopdfqtEJMGa94+YH12qdoCqsotD3LdunX85V/+JZ2dnTz55JPMmTMnpgIvFXyXy0VbWxvt7e389re/5Tvf+Q7r1q2jo6ODgoICfvjDH/LVr36VG264gYyMDEWmkc/Sh10kxx/su/GfGnq+Lrl5cnKyYtM5HA6SkpJwuVwMGzaM5uZm1q9fT09PDzU1NWRnZ39ibHcoQiJPiTplg9NrQ/JMRo4cidfr5e233+bkyZNUVFSQmpqqRE8H6zMY0C1Iz7MlRPJ6vbS0tHDy5EmGDRtGZWUlWVlZMa8LBALq0MOf/OQnHDt2jKamJtrb26mpqWHGjBkUFhYqI5feqXhynQcvUcLVwnf+otDntuNFPnShSYDy8nLy8/MV+7C3tzemRz1UIUU2PTqRe5Iak7TaLBYLlZWVLF26lFAoxK5du0hNTWXJkiWUl5eTkJAwaNOZATV2veIpD+TDDz/kgw8+ICUlhWXLllFSUqIWlxTtGhoa+P3vf09PTw/vvPMO7e3t/Nmf/Rnz5s1jzJgxTJw4kZSUFLUb64IGEqLq6jfyS768ax3xi1M/9UYKdNKamzZtGsePH+fw4cNs2rSJvLw8srKyhnQ6JNetrxW4RNiKVy2y2+2MHTuWBx54AIDNmzdjs9lYunQp5eXlak3p/f3BgAEn1eitiUgkwqFDh9i6dStZWVksWLCA3NxcfD4fkUiEjz76iD179lBXV8eqVavweDzMmzePiooKJk6cyC233KIGY/RKqHh0XWxBQjJZlBKuXevQyTGSp+oeXW9LORwOpkyZwv79+1m1ahWbN2/m1ltvJSMjQ1Xrh+LmqdcmZH2Ikco60c+qE/Wa8ePHYzabee6559i5cydms5n777+fwsJCtd4+TdQDrkxtY0Cr8TqbKRAIUFtbS0NDAzk5OUyePBmr1Upvby+HDx/m1KlTbN68mffeew+bzcaUKVNITk7m8ccfZ8yYMUpIQUe8Dp1eZIJPqsbE7+DXOuRZxavN6D1kmQPQp/7keX8eFXowI74/Hs+0k0hQQnxJc8rKyli6dCmrV6/m7bffxm63M3/+fEpKSmJSxXga91Vt7HBJE152yvXr17N582bKy8tZuHChOlBh8+bN1NfX43K5GDt2LCNHjmTRokVkZGSQmZn5qYau449pMAzm/uiVhtRYxNiHDx/OpEmT8Hg8HD16lGHDhpGYmBjz81czpFov04LV1dVq43vzzTfx+XwsWLCAyspKxRORvP9Kkm4G1NglRJQCjxTaiouLaW9v58c//jG9vb3Y7XaSk5O55ZZbmDFjBllZWZSXlysD19tmBv60EE/tdDrx+XxYLBauv/56Tp06xUsvvcSbb75JTU2Nkgq7GlmJsnnpZC6p3kv7uLq6GrvdTnd3t9Klf+CBBygrK4uR076StY0BzdnlGODm5mb+67/+i40bN6pRQiHU5Ofns2zZMmXkIpggXGThLct7Ghg4OBwOwuEwqampFBcXEwwG+fjjj+nq6qK0tHTIqNf8sYgv1skkptfrxWq1quGqZ555htdffx2Px8P3v/99daSXXhO4EhiQPrsUf8LhMKdOneKnP/0pK1eu5MKFCyokt9vt/Nu//RsLFixg2rRpFBQUKP0vXUBCL8YZvwbulwwYSe6anp6Oy+Wirq6O2tpaxTC7Wr8buBhRut1uotGoqlnoRJpwOExaWhqjRo2ira2NtWvXcvbsWcaOHUtKSkrM+r1qc/ZwOMzRo0f5xS9+walTp9i7dy8tLS04HA5uuukmbr31VlJSUrj55ptJSEiIOShQp7e63e4+i1cY6D9IyCrDL1arlYyMDHJycvB6vTQ0NNDV1aV67lczdEUe3cPrKjhVVVWsWLECu93OqlWrSEhIYNmyZeTm5pKQkEBCQsIVufYB+Wai0ShtbW2sXr2axsZGkpOTmT17NuXl5UyZMoXrr78ep9Opind6/1vXOevp6cHlcg15xZChCCmq6iIdosdvNl88QVc01q9G6F7cZDIpzT2TyaROttW7O8XFxcyfP5+Ojg42b96M1WpVI9tXit8xIMZuMplIT09n4sSJdHd3K23ysWPHEo1G2b59u+LIC6LRi7mRTBW5XC41Rml49YFFNHpJm06M2eFwUF9fj9vtJhgMsnXrVs6dOzck++x9gVTf5VQc/UARYSAK3Vb0+aLRKKNGjWLPnj28/PLL2O12cnNzlfrRQKNfBmHij07SEY1GaWpq4qOPPuLQoUM899xzfPzxx+pIHUDx12WHhFhVUD1U0skNBgYGeu6qE6KE8hyNRpWG/tX+vcSfHxiNXlIxkshHUh2ZKPT7/UQiESoqKnj66aeZPXv2FTlI8gt7dvHAkq+JsUqeLfzhH/zgB0QiESUIoEsyy/vov8dX3HVevf7/Bv700P1B/Mz2YKOE/qnxab5RX5uiaAyX6LdiF3Kq75Vibn5hY9d7h/GGGAwG1a6WkJBAdnY2d9xxByUlJQBKBFB03q6VBWPg6oQYu0xqSgdDQn+r1UpxcbEauBlo9EsYLzepjwVKESMUCnH69GkOHDhARkYG1dXVpKenq9xPn6oyjN3AUIZEuboYhswZCEdEinxXosjcr8YuhBe9lyg3KcQDOUlEZtrhYlU3HA5fkTzGgIH+gJiR5PR6N0nvKAExh4wOJPqlrC1GrXt1nYwRCoVUKAOXCnL64MW1UNwxcPVCtwH9UJJ46XGp2F8J9Mv2olco5Ub+f3vnFhNX1cXx/5kLM8PcoYdrSimXoLXUWiAlJthKPxsCWogVjaRRY9M3NfbJFx989/LgW9/qi20s3sBqGksxlgBjG+vUCMQ45SrlUkDmcubKzPdA1mbPoSD0w8+Zzv4lTZsyc5gzZ6+91l5X3kOvdqzx3Wf4dlG8l1MgSEd4Q5nWMyWB3c+v9f9kx0Jv6vAbXyVFryEnnCRJbCwP3wRSCLsg3aFzO7A+l36z+vb/Bzt2ZgfW+oxLkgSv1wuDwQCTycTO7dT3jZIKEokEew/fvlcIuyAdId8V3/SCes7zw0X/rTW+obDzxfbAevMEWDunkJlOgsu3MiIBptgiaW+1WcNPXRUZcqkFaae5uTn4fL51cXadTgeHwwGz2Zz0/NSvexi4X4iYlwf6Oe+Z53NReJkg1I0t+OuSHPFySP/e7ne64Zmdih74X0J/+GQB9c2SqUIZRLyQ89VrvKDzX4zQ7KkHPfPu7m709fXB7/cjOzubzQCwWCyora1FdXU1CgsL2Ugt9VglYPNRTKkOv075DY33tvMJNrTOKVKlbslG11tcXITZbGZzEkguVlZW4Pf7YbVaIUkSa/BJ3/t2j7wblrjSTanP2uq0yWAwiEgkwlpA0c0Cq8IfDodZV1e1RqfOncDq5sJXuwlSB3r+c3Nz+PHHH+FyueBwOFBfX4+9e/ciKysLLpcLXq+XbfQWi4WtEbWmT8fnq04ZVssFsOaUBrBOSVKdBynERGK1Ndvs7Cx6enqQnZ0Np9PJRmnR0RZY9egvLS2ht7cXo6OjKC0tZb9nO/Ky4TZLHnPe2cBfmOZ587Ov+Xx20uSk/SmHmk+j5b8sXhMIUgt6RnV1dSgrKwMA7N69GydOnEBHRwfa2tpQVlaG/v5+fPLJJ7h+/ToURXmo6hjomMpra35EFu9kpiMpXzvAKzpKNpuamsL58+fZdXirgf42mUyIRCIIBoMYGhrC7du3H3hs2d/aVKSpQ6EQ86DzWt5oNLLRP3wmHX/e4Gda08/4HY7O+nyITpBa8BNSaGopbfQ2mw1tbW2IRCLo7e2F2+1m64A/yqnz6tMNtQ/ifoorFAqhp6cH586dw7lz59DZ2Ynh4WH88MMPmJubY3nz8Xgck5OTuHz5Mg4cOIDi4mJ2PVKaNGBTkiTWj1Gn06Gvrw+BQGDbG+mGZ3Ze8HgNT8kwdKbnM4Xm5+cxMzODwsJCOByOpGwiPgTHJx9Q4wPq4ZXOZ7qHGXUNBFl1wKqVl5ubC71eD7/fj0AgkJQ0pXb2pit8Mgx/b6Tll5eX4XK5cOHCBfh8PpSXl8NqtWJiYgIejwcvv/wySkpKIEkSJicnMTIygvr6euzatYud1ykZh5QlDa+Ix+Oorq7G8PAwent7sX//fjagdKtsKFlkhlBiP9/RNR6Ps2F/9MGWlpbQ39+Pvr4+eL1eZsJTHJ2PNwJgpkx/fz+6u7vX9SgXpBZ0To1EIixqQl5lk8m0Tnvz5i2fPp2umzl/L8DamZzuyev1wuVy4eOPP8bo6CiOHTuGt99+Gy0tLfjtt9/g8XhYNmkkEsFPP/2EgYEBnD17Fvn5+ezaBoOBWcvZ2dmshsRkMsFqtUKWZeh0OszOziaVhG/pHjb6wcLCAjOvQ6EQfD4flpaW4Pf7WcycOpMkEgkMDg6iu7sbBw8ehCzLUBQFi4uL8Hq9zBPJlwECYBNC5+fn4fP54Pf7xeCGFISOXJFIhFUq6vV6RCIRZk46nU7W3EJ9nAOSHVzpDN0DDXukTeDPP//EZ599hpGREbzyyit47bXXkJeXh+rqanR0dLBJMVTxRkoUAFN0wWCQ/VEUhTn0qHLUZrOhvb0dTzzxBDo7O3Hnzp0kp+DfsaEZf+LECTidTtZ7jLyslZWVeOGFF3Dw4EE2yC4UCiEcDkOSJIyOjqKrqws3b95EMBjEmTNncOrUKQCruyMl1uh0OiwsLKCxsRFmsxnvvPMOPvzww4e208nDAE1s1Wq1CIfDbEpuIpGAoiiQJImFkKgjMLA2mYcaO6SrdgfA7pvfxABAURSMj4+zoi7aIMPhMOrr61FZWQmz2YxQKMSSzAKBANsko9EoFhcX8dVXX+HKlSvw+XyIxWKw2+346KOPkJuby4Zs0u/b7ne5obBPTEzg7t27eO6551BTU4OsrCzcuHEDLpcL8XgcpaWlyM3NxcrKCq5fv45ff/0Vzz//PPbs2QONRoNvv/0Wo6OjuHv3LhNwfuB9IrHa3aSkpAQejweTk5P466+/YLVak5r6Cf59+MwwOt7xceRAIID5+XmsrKzAZDIxrU/PkTfh0/m5Uj0HFbSoK93I+67X61knJvJZ0abIh+TIRCdBv3z5Mi5dusTmJAwODiIUCiEajcJoNK4bVLodrQ5sIuz0gGpra/HSSy+x8co9PT1wu90IBAKwWCyIRqMYGRnB5OQk3njjDTidTmRlZcHpdMLj8SAajbKmhJQySB+ShthXVFSgqakJX3zxBU6ePIny8vLtPwnBPwqZruRAIvPS5/NhbGwM165dg8ViQVNTE2pra5MSrnghT1dhJ687n/LKn9/5ZBneVwWsRTL419D7SOj9fj9u3bqF4eFhnDp1CsePH8ehQ4eg1+uRk5OTtHkQO5ZBFwqFmHc8Go1ieHgYN2/ehNlsxpNPPgmr1Qq9Xs92efog/Jk8Ho/D7Xbj4sWLKCgowNNPPw273c4+KJkzJSUlaGlpwenTp3H48GGUlZWl7aJ4GKGF7nK5MD4+Do1Gg4mJCXR1dcHhcGB6ehpzc3M4fPgwampq2OhisgT4fvP3SzdNB2htq7vMkLaPx+Os5oM89HzsXZ0GS2Y+sOb8pLO5JEmoqqpCQ0MDVlZWkjraktLkHaRbZUNhJ8/rL7/8AkmScOPGDVy5cgWVlZV48cUXYbfbWfycPjjFCfnumlNTU2zccjQaxbFjx2Cz2ZKa9NEXw1cMCVKLaDSK6elpFBYW4plnnkEsFsPvv/8Os9kMnU6HlpYWPProo8jPz4fFYklKEuFJR0EHkkuz+SMJaWaz2YyamhqMj49jaGgIw8PDqKqqgsFggNfrxfj4OPLy8lBUVMSuR2ue5Ihf+zqdDoFAAAMDA3jqqaeQnZ2dFM16kP4Pm9azx+Nx3Llzh8X7SkpKEAqFMDIygtLS0qTzB98GmnY4jUaDhoYGyLKM999/H5cuXcK+fftgt9uZVgeQdLYTpB6UydXa2orGxsakRJmsrCzo9XpkZ2fDZrPBaDSuK/O8n3ZLN0jI1E0pJGl1Dt7evXvR3t6OQCAAt9uN8+fPo6GhAWazGT6fD/fu3UNtbS1kWWbVcBTClCQJNpsNBw4cgNvtxuTkJPr6+qDRaDA0NIS6ujrmDCdLmxTqdtj0zG6323HkyBEcPXoUWq0W3333HT799FNcvHgRdXV1kGU5KaQSi8WS8t21Wi1kWYYsywgGg5iZmWFZQRqNBoqisJ1NhNxSG0mSkJ+fj5ycHEiSxPr8U481eg2tA97aU4fb0lXoeb8D77SkKMRjjz2GM2fO4MKFC/jjjz9w7949SJKEoqIiHD9+nCnIcDjMslHpiORwONDc3IyFhQXcunUL33zzDUpKSnDy5ElWTZhIrA5bURQFsiyz732rbJpBFw6HkZOTg6qqKkiShNu3b8NgMGBmZoZ5CCleyHeI5U0UMj3uV/ZKHkqK1/5bzfMFm5NIJOD3+2EymVg2F0VWqHiJd0KpTUzej5Puz5fWMu+DoC7KWq0W+/btw5tvvskq1GKxGCwWC3bt2sU61lgsFhiNRoTDYfj9fuTm5kKj0SA/Px+nT59mYWwqKCIN7vP58PXXX8Pj8aCjo4MdCbbKhsJOgki7Mt1cMBiEyWRi3kZFUbC8vAxFUVjnTHqgVquVmXX0er5YhpwOKysr7ObFmT31oI2ZwmzRaJTN5OPXBx/z5YtCeCWQrlqdt1jU98JXdGq1WhQWFrK1rSgKG+pIyi4ajeLo0aPQaDR499138d577yXNgaPX0AQa+j2KomBqagqBQAB5eXnbbkm9qTceAD7//HP8/PPPzAO7e/dutLW1QZZl+Hy+pGF+dPaORqMwm81ob2+H1+tFb28vysrK8Prrr6OgoICFY4LBIPM2ivLW1IWv+KJNm6wz8iLzgg+AzezjnVnpLOzAWjkpZYTGYjFm4fJ9FXnr1mAwsPO5wWBgGYYFBQUoLi7G2NgYKzLjnXVUd6IoCqxWK0KhENxuN4xGI9ra2mCz2Zgy3up3uqGwv/rqqywDih5iVVUVKioq0NraCpvNxlpP0ZmCsNvtaG1tRXV1NSYmJuD3+9HU1ITW1lZYrdZ1O/3o6Ci+//57NDc3o6ioKK0XxMMKCTZvuRF8xSL/7NTJNPxZPh1RN57YKPVXLewUnqbkMpKVoqIiNDY2YnBwEPX19SgqKmJOa36EFL3X4/FAq9Wivr7+gSbBbtiWipwvvLalRH4Kt8TjcSiKgqtXr2JgYAD/+c9/cOjQITYEgh4w5VOrm+7RELwvv/wSH3zwAbq6upCXl/fQj/1NVygXXD3mC0BSPH0jKNebVwzpAi/cJLTkl+JHmFFuAf2bfk5HYIqRA6syNjY2hs7OTjQ3N+Pxxx9HIBAAAOYDI8sgGAzi6tWrCIVCaGtrg9lsBrC9zj8bStX9BE6d8kdhhyNHjiAYDKKzsxOyLDPtzQu3uiiCGvLNzs7C6/XikUcegcFgSNtdPxPgvb9qz/RWnls6CjkP3bP6rKy2RO/3XVD7Lh6DwYDy8nK89dZbLLRGr+GvaTAYoNfr8eyzzyIejz9wOvmmobe/+3/SzkajEQ6HA0ajETMzMyguLobVamXhtVgsxjaASCTCziXhcBjXrl3D0NAQzp49y5IxBKnJVtbEg7w/HdjKZ3+Q++M1/WbX0Gq1MJlM274+z47YyzqdDvv374fP58P09DTKyspgNpuTzHd1iiBv9tlsNlRUVDCzKJ0XhUCQqvzPfeMpzhgKhbC8vIyFhQU4nU7IsswcE1lZWUnHAvLUUh3wwsIC9uzZg5ycnG3n+woEgq2xI8JOGUHUrkqj0bCEGz4/mgRZ7ZWNRqOs/Q5ZAgKBYGfZEWGn5hZUPENZVpQFBKyV/vFdashzyXftELF2geCf4X9WoSTQfBiCb0HF97FT5xOTJ5dGOqd70oVAkMrsiIOOhJjignzXWeqlxacT0nv4xgZ+v19UvwkE/yA7MtiRzHi+Cw2ApMQDamfEm+tk+pN1QGE5EWsXCHaeHZviymcMsYtzWpqKItTJGPxr+TRagUCws+yIsAsEgtRHxLgEggxBCLtAkCEIYRcIMgQh7AJBhiCEXSDIEISwCwQZghB2gSBDEMIuEGQIQtgFggxBCLtAkCEIYRcIMgQh7AJBhiCEXSDIEISwCwQZghB2gSBDEMIuEGQIQtgFggxBCLtAkCEIYRcIMoT/AkgpCO9zQ1WoAAAAAElFTkSuQmCC)
The median AD of the triangle ABC is bisected at E and BE meets AC at F. If AF:AC =1/k then the value k
![](data:image/png;base64,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)
maths-General