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Home /Doubts and Solutions/CBSE/Class 9/Mathematics/Circles/Angle Subtended By The Chord

Angle Subtended By The Chord Free Doubts and Solutions

CBSE - IX - Mathematics - Circles

Prove that the circle drawn on any equal side of an isosceles triangle as an diameter bisects the third side .

Asked by Vikas 12th January 2018, 10:54 AM
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CBSE - IX - Mathematics - Circles

Please solve question no 12 with proper explanation 

Asked by adityaahuja099 2nd December 2017, 10:05 AM
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CBSE - IX - Mathematics - Circles

Please solve question no 8 with proper explanation 

Asked by adityaahuja099 28th November 2017, 5:41 PM
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CBSE - IX - Mathematics - Circles

Please solve question no 5 with proper explanation 

Asked by adityaahuja099 26th November 2017, 3:41 PM
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CBSE - IX - Mathematics - Circles

Please solve question no 4 with proper explanation 

Asked by adityaahuja099 26th November 2017, 3:37 PM
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CBSE - IX - Mathematics - Circles

Please solve question no 1 with proper explanation 

Asked by adityaahuja099 26th November 2017, 3:35 PM
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CBSE - IX - Mathematics - Circles

Please solve question no 10 with proper explanation 

Asked by adityaahuja099 20th November 2017, 7:57 PM
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CBSE - IX - Mathematics - Circles

Please solve question no 7 with proper explanation 

Asked by adityaahuja099 20th November 2017, 7:50 PM
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CBSE - IX - Mathematics - Circles

Please solve question no 6 with proper explanation 

Asked by adityaahuja099 20th November 2017, 7:48 PM
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CBSE - IX - Mathematics - Circles

In the given figure if ABCD is a rhombus diagonals AC and BD intersect at o   and he is a point lying on the circle with Centre o then the sum of the measures of angle BAE and angle EDC is?? 

Asked by shriya.pandey182 20th October 2017, 11:01 PM
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CBSE - IX - Mathematics - Circles

How to prove that angle subtended by the chord are equal to the chords?

Asked by Preeti 11th March 2017, 7:38 PM
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CBSE - IX - Mathematics - Circles

A circle has radius root 2 cm. it is diveded into two segments by a chord of length 2 cm.prove that the angle subtended by thechord at a point in major segment is 45 degree.

Asked by Snehal Ambekar 12th March 2016, 6:30 PM
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CBSE - IX - Mathematics - Circles

Prove that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Asked by mkmishra101 3rd March 2016, 5:38 PM
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CBSE - IX - Mathematics - Circles

I didn't understood the sentence " The degree measure of a minor arc is the measure of the central angle subtended by the arc." Please help me with a diagram.

Asked by parthapratimdeori1998 17th February 2016, 11:08 AM
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CBSE - IX - Mathematics - Circles

please ignore tech team testing

Asked by Srinivas 3rd September 2015, 3:44 PM
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CBSE - IX - Mathematics - Circles

qus 1 -Prove that if the bisector of any angle of a triangle and the perpendicular bisector of its opposite side intersect, the will intersect on the circumcircle of the triangle.
 
qus 2 - what is circumcircle?

Asked by Varsha 25th January 2015, 6:36 PM
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CBSE - IX - Mathematics - Circles

<div>In the followin figure, A is the centre of the circle. ABCD isa paralleolgram and CDE is a straight line. Find <img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=10760cd90092037cd4f09dde6a7d7bb7.png" alt="angle" align="middle" />BCD:<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=10760cd90092037cd4f09dde6a7d7bb7.png" alt="angle" align="middle" />ABE</div> <div><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEFCAIAAAANKyW7AAAgAElEQVR4nO29e5Bs213ft/o1PT09M2fO815fkAQiip2X7SoqMVUhlYcfiWVcBhsHqbBMKkS8AokwUjByycIGERtkOw4GFMfBJKRIME5hQpBMoig8LMUORpYSWVxdIe7Vvec5M/3e77XX+uaP7+7fWad7Zu7pud09PXN/nzp1qqd7T8/u3Xt/92/9ngaKoigKAMBc9A4oiqJsCiqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIiqIoFSqIihLiAAcPeP5XPQbggZIPg2eUK4YK4tXEOZfnuTy21gLwvrqEx+Oxcw5AHMfj8ZhPFkXBbbjZZDI54/3jOOaDKIoA8P3TND3jV0ajER9w43nyPOc+lGUZPl8UhbW2KAo/he/AfZjfYXl/7tsiOJuN4AtkHg4WzsLCO1i4EplDDPSSCUrAwgOTPFdNvGKoIF5lrLVlWVL70jR1zoUy1+/3+SCKIm7D/0VHytMB0Ov1kiQBwP8pT+4UKFK9Xg9TvYuiyHtPsRPtlv0BkOc5n58RUP46n+T/8hkBFEWRJMnMGz79AQMS+AypR4l+3I+RwDvkgEcOHPkiBZB5ZBhP4lyNxCuHCuLVJFQEKsiDBw/446NHj+Qlay2FjP8fHx/z+SiKxAY8EQorDbp+v2+M2d/fN8Y0TsEYY4wR444aGhLHMQ1MkTaxE3u9Hv9QHMd8kp8uyzLZh+FwCCC0dk+zQ8/EZvGxS4ZIC1jEZZzTFHRwBRKLvncpgLSERQmoIF49VBCvMmVZFkURiqM85gOqCeVJjMcoimTpas6kXq+32+1OpyO/bk+B78zf2tnZ2dra4uPt7W1jTLfbFUltt9uYmn5FUdCoDAnNRj6WD2WtpZ6KGbsgzvsEPkNR2MGgQJnBZVlRpg4OJRABh0niUosCJfDFw0cqiFcMFcQrS1mWohRchL788sv8kU63OI6TJBHHHxWt0+m02+16vU7BOuPNARRFIevrs32ONEvTNBWjUvYBU8tuMBgASJKEliZ3oNlsZlnmnPPe53nOvxLHsfw57n+e53wra+3R0RFfWtxIdEBRxoO/9xM/umtMfbtpmnVj6vu712um/ra3v+PeJEoBeMT9uASsWohXDhXEq8mMiSThlNFoROGgMPEB5Y8GGh2LfPVV4yqihlxrn73KfvjwYbgn8v55ns9bc1wO8z13dnYojjQeBecc1ZC/PrO33nt5k6fGFTaBzz7yUx/aM8bUTev6dVNrGtPcqjeMMX/gD/+Rj/9/n02TEh5Z6XTJfPVQQbzKcL1Mpfj85z/PJ8uy9N6Lyuzv74dREYmTcK3qT0EkjJoYxmROg2YgAzvztttoNIqiyFrLNxTdpNRmWUbdNMbUarXQeuUfZQhb3pbG5jlwzsJnv/h3/vp1Y97w5V/2S7/+iVHm4fH+935vzRjT6vzshz9WAvAYJ2nhVRCvGiqIVxOaeGIGlmUpbjuuRmdSUmhqUVDkpaeJq0jWS5i1M0/4i5SwPM9PFFDZZwTx6BN3IPRm7u3tURPDGMt86OZVcR7w2T/4sb/8XMOYmvn1Tz2fAc7j1/6PX+pu1U2j88Mf+ukcGMdFVqoaXkFUEC8H3nsKkLj8RE2cczS+JP5ApxsfiwLiPHl5l4aiKK5duxZajqKGvV6Pa2fnHOWSB0dsYYl9A4iTAj772E/90G1jOp3ur3zyc8cJLPDd3/ZNB52Gaey+OCiPYj+x/hwhG2XzUUG8TIzHY0lbobMvTMEjlMVms8mIBKZ2Fo2mK4wsk2kwGmPyPJdEHKbslGXJZ2hO0nSV5f9wNCmBuP/wH/7En3/WmHq9aeo3TGPf1Jo3ts1X/d63HEcYAxGQAiVwfNy/gM+prBIVxMtBmDwo2YIAyrKU5GQ+w0QWTKMKVExuI+pwJbHW9vt9Sh6PBg3GJEkk/EJoJ96/fz9NU7ENi6LwgAXgs5//kW/9irqpmabpvtE0r5t6c8eYHWNM4/r/9amXh8BhXtKTqFwxVBAvDdS1oijEy8aVIM2cLMt4/UuZh/wioyjnysu7fITxdD4wxrRaLQCDwUDuDWECo1TsjMbJMAJc9g9++Ju/3JhuZ/8Xf+1zxx4pML73mS+70TL167ff8tUPPMbAF+8+UkG8eqggXg6Y4xIGPSQJWdKbRQuKoijLkpu98sorfNJ7H5qWVwzvvXPu8PAQcyXVcpQ6nc7+/j43TpKEPgQ+TpKEFmIOIBn9P//9e95kzE5r92OffDAEJs5nR8//5T/3zfXWHXPwe/7+P/rkECgBnBVUVy4lKoiXA4qd+AH5IxNQELjP4jgOQwTEORfH8dkh48vOTCA7z3PeCaiGEo8aj8f0riLoJSE4jxwoJ/1/8nf/87cY0zCtX/300SHwYDKBe/iub/oTpnbDdL7iEy/3/nlvUAmiGolXCxXES0OWZVwjMxevVqvleS6BY64QJbQqnWAktIpXyxO87Hzxi18EcP/+fXkmjCCHuUEAjDG3bt0yxlhredB6vZ7ziC3gsl/6kbe/2Zi97Wsf/vjLD4EYeOE3/rev+t3PGHPwpt//1i/k6AMlkEeZCuIVQwXxckAnYKfTMcZQFkX7hsOh+AdZ38bH1lop1bjCCTckTEIEEMdxWATNY8WYkhiGfNIYs7W1VU5jJBaALz72k9/7Jcbcunbb1J4xzQPTqO8Ys2tMp/vsL3/88z1gBIyTXC3Eq4cK4sUgciaalWUZe7RIjrQEhXm5bm9vi3fsaseL10CYLp5lWbvdzvPcOYwnKeD+ux/9L7eN2d+9ZmptU2tt7XQaxrz967/WA3GB2CEpy6pTrHK1UEG8SBjloEc/fF58hVwAMnwcxpTDboDK+ZDoPO897XZ7e3sbwbHl7cd7H0WRfEdyAwt9EcqVQQXxwqDdJ6vdsiwfPHhA9z/DILJGlg6vXA4fHx87587b4UoBpj7WwWAQ3lokdSnsukiofWmaSi731XbIvm5RQbwYkiSRqgk8mWsdRREvRQZDmUPD3tcIMrTP2xRaqXjxxRf5QJLbJUux3W7T6yr2IA8+71JhetPa91pZLSqIF4YoGjUurDlhJy4pSZ5p/QKAxRjnaF6gkDAJiV0dQ4uPK+hGo4EgbC2Z3rKlHv+rhwrixcAFr3OOGpfnOT1WbI9KcQy77T948CBcXCNYayvnQI6edEVDMJlLmteGLXLlbsRmtLpkvpKoIF4MoesqrL2jXx+BGZJlmcRYOEEJTy6xlfNRlqVE7aMomkwmYokzkMLHHG8g5X1h17KZbHDlCqCCeJGIDzFNU0phOPdOPP0AiqIIE3T4QJds54ZaNuORIKKS4UzBTqfDjt8IvhE10q8eKoirRQwKjtycaWrPa6/Vakkx2YXs5OuQM+ZW8zsKy8alGvrGjRv8ypjOLS9Jc1x5w5m7F3/ryqfHXwFUEFeOcy7saC+hSamUkP77anGsmfm51cPhMMw05IPt7e1arcZvp9ls1mo1AKPRiBME2WVDenSHrSXYbCKcO6hsOCqIq4XVxAhMRWut9Bqo1+vcLEmSsyc6KcvljLnVvFFRxTjFRdbOzA8NIy30/NZqtYODg+FwGPbiZneJsNfGle/RewVQQVwtskqS1gy0EAeDwc2bNzE1IpQLYX5utfgWqXT7+/uUS7Hid3d3MU0RpfCJXc9MHX7LM7c355yEZZRNRgVx5bA4TH50zjGaXJal9KThtDnJdFPWwIlzqymRmEqe9BOy1nI1Lf3Wut0u184A+v2+rIuNMRzriukoQa0pukSoIK4WXiSidGmayoJrNBpJcxqNF6+Z0+ZW83bV6XR4uwrbKQK4devWcDhkIj2Lnev1ehgo45biHeYgab75vXv31vPRlNeCCuI6EKf71tYWnYlhWq+089Io85qZn1vN25VUp8x4/eRmdnh4GM41ZCCFXc0xnT0tr4oyKpuPCuLKEZmTy4lmI5dm4Xh4ZW2cNrdazEYZcMhBVLQcwwhJmFrPCX/hSOj5PxeOSFU2Fv2GlsZMz2oGJeX6kYtBzcB1Il1q+O1Ijwz5FvI859xqSZIX1UvTVAY6I/gGiXTc4IqYmgiAFS8za23nHE8MGQ8bJjBKYEcib/K74TAsTPMZ1de8OlQQl4M0C+ApG06Rz/OcSbySlqGsjVB3+B3xG+EzNAw5aQDA3bt35zvvytgG/vjSSy/hydyAoihkxM38n2bjbv456WOEYETq/A7LSRLeO/v9vuZ1rwEVxKUhayVeeGHYUZJ1xU65oH183UF7kPnSlC3vPb+gsO1uHMcznb7G43FRFKwZL4ri2WefldI92m53795FkHPDNEZ5QwBHR0f8ohmEEWuR78zHu7u73I08z/v9Ps+T8Xgs2pfneZIkfJ+7d+9yDu3MWEFliaggLodwVnLYWkoKUUg450RZD3LA4zie9+eGxiMAa+2MT4PGILeXwQPee7ElZ4Y9cMs0TaUBB3eA/4vS8W1FBBnaDm3MXq/HvyX9kLSXxBpQQVwmcl3x2pMOr3jSPaRrn7XBgz+ZTPjVhMENlgzRcGOl+UwHDelQKerpvZe5AvxflgXMu6Yyht5GMSFDnQ0HYIWbWWtl97g97dCiKMTAZJBnOUdHmUMFcWnIWc46h06nA2AymUg3Zp7izjm91a+TOI7D6aPyWJbA4dchvsVQv1qtVp7n4/GYW8pLFFkZ+DezMsiyLFwdY85I5A6kaTqZTGbSUY0xBwcHVEaRwtDCVVaECuJy4MUgA/OYd0arIbwkBoOBxlXWiSTHXL9+XQw3mnVFUdDxFybfIAhrUAGZbRO+52QyCe9qSZKEoZg0TXlrlD/HV6VwU/7cfNuxMGWHZ1S73RZ7lmoYNgpRlo4K4pI5OjrCXIoGR4xKnaze59cJ709JktD+mike55MUKWl7g6kZWJblzs4OngzOIGjwJatXlrWI9VcUxd7e3mQykbVwuM5lYqP3PnQoU+nClTvL/mT0Fcs9JadHWQUqiIshZ7yc37Kikdv71tYWtU99hUtHvHjS6z8cB8rIQ9h8MJxDj7l87BPhq6H38BwuDtp3tVot7ER7Dvg+YSxod3c39GNKImSYKC7eT0474O/KiSqnrp6f86ggngcmQ8h15ZyjP4grLG3ktQa4sJ3vrBWuXilnrMmjn+5p5uTxHRiHuXHjBjNdzrGHbOrRbrdlsXw+WaSPUjRxOBxKsg4/NXVNcnH4ZJZl9NhInx6+yikUukY5DRXEhQmvEF48cjWGqbZsYHMhe3iFCeOzYvdJ2EqenKmTC028s3vPhEUgnLp3vrZd/Oq995wahvMOYOH+OOf4oN/vhy0X6WHkO8ttWJbhVD1aiDxF5W5RFIWGqk9EBXFh5IoKLRQW6hljwkEoyooYDodUgeFwyDQ9uuR4o5JOClmWvfzyywjWhnmeP00nrrIsoyjqdDpRFJ1PyLgnMl9bdnhRWEc4czrxzY+Pj+m47HQ6xphWqyVWoRT8zfwifZd4tbvC6xkVxMUQBZQ6BCZDHB4evuENbxDLMWwDpSyRMwSCElar1QaDwUy+CwCul19VBcLE7Nfei4FxkocPH7Kt7LlrkOdvAGHltZRC02Eqjdn5P/dBnInWWsb9oBVTJ6GCuBhZls0nYQC4efOm5LWFdWDKcjltCclKjxkfBb8F5taEUviqHjRJqudK83zCwdshTbaHDx+eT15PcxGwAFGyf8JeFdvb2+wfgSDXB3NNvGdi3ApRQTwPkgsm/V/D051XQpZlaiGughODDHxMQeQ6lwffOSeJMhJ7PQOpt5MquvM5guc1qNPpvJYpAjNBJDwp65Q2npbS2qdWq0ki+kwRvSYznoYK4mLwMpPMXgCj0Whvb4+vhp2x8aRVoiyF09JQOP4JwEzvA0lJCVvInB3tHQ6H29vbcjM7d0BWdkNmnM60w3kaTkszCuNIhGej7La8tLOzY4zZ29uTihpMT2C9Yc+jgrgYMgiFTCaTvb09naa2dGjC8I5Cy07mz3ADid6Kp2IhQpkLMxlpD+7t7Ul+X/h1v3a4z1mWSQ31Et/8DOgE6Ha7eLJDnfZhnEEF8TxwIFSWZdevX9eUrhVRlmWYMSc+Lw4C5UBkXqjnviHNxGGlLZj0+g1VY1lQE8WCe/To0dpkMU3TRqPBNMYZ74H2YSQqiIsR9nrCMgKRyomwh6AQSoYccxaGn88vEXbT4lgVWdgyHCFSu9xQ7GQyuXHjBt9cOnKvh+Pj49Czub+/r30Y59Hr+TxEUcSsQ/44381Jee3ICFAZO8PgKT1fUr52bk2ZTCZSPcJsmziOd3Z2er3eSm2iwWDQarXCSQZr8OXNhJjv3btXFEUURdqHcQYVxIWRQCQFUbK6lKUjBuB4PObR5jqarzKfBud180nZr0gq2xFiOuSEU/SyLFu6V4R/Re6j67ETh8Nh+EGkFBrahzFABXExeAL1er04jq9du5am6WvJpVBOI8symdMkJsyJReLnM8/TNJVyIz7zwgsvhN0SydIlQKbRrllcpOp5PB5LpF7aPmofRkEFcWGk53tZllIjcdE7dTXp9/u3b9/G9D6UT+FXQMOqLMvX4rJIkkSu/P39fUy7MFAvGGteou9MJtC2Wi0+sx6tCa1gTI8kn9E+jCEqiAtD+et2uzxFVA1XAfsGHRwcDAYDCtZMKFnGm5wbOtH4WG5yMplPNlv6elbGlmLqb1mPJoqs37t3D4HnR/swhqggLgYvIbm9I2hIp5xB2BZwpvdMOJpOkj/Wk0gceiTXkzDAD8vg9f7+PsurN/D8OaMPI4KuummaigM3HKIg869x2fowqiCeB3E2hS3nlLMpy1KuqCiKONCdP8q0GQDGmHq9vupSM2mNI/uzHkF0zknL7vnhBBvFiSWSLJTGk4EsJqKFTZElp/3S9WFUQVyYPM+73a6sOKBdQ54CsRfYrpVIoTGNiEajIaFkrL4ZgQwglVYO64GfjgtSPrOBJXSnNdHgj1xKdzodji3kS1yJs6uQWIuXrg+jCuJiMLF2pnRfS/deldCgoPNuZvncaDQYG6E6rKddldgvW1tbTLJZ7vvPw+oX8ccZYzZz/XhGmzV5MkmSdrvNckAulWY+Szhv47L0YVRBXAzmY4dtsTfw9r6ZvPjii3wgfsNwjSybsXaCj1d3IcVxLGk3tNTCAqSVwr9779497z2bcm+sRsz3YcyyjDIXaiU9jGLwyrqYwfrL1YdRBXEx+K1zoSdWj6Yivio8VoPBIJyFJMtG/pimqajSGpZa/NaSJNne3gbgvV/DMBx+Ct5EKTF7e3vL7R+xFE7rw8jH4RyuMFAu2d1lWcoY68vVh1EFcTEkm59f9uuhunNZ8Ihx9NJ4PG6328zn4KtpmspUa6x+KBIv4yzLtra2ZubHr5pQDsIC0M1kvg8jD53kA4Tdcehh7Ha79Xqdn+vS9WHc6C9jA2E+NoL73kWbhw44I8Z99quv+rZLi56HaYNZlrXbbelLGMdxWBSBqWSsOl1D4gOYmmxruL1JdNt7z48j3W03irP7MEq2Jk14OW78isNMpoXSpzxQAp6PPOAA7wDn4UqglI34D84v7/wUVBBPRgKgYQLdORp8rhgHWKDSCw94//iE8XAe1sNWuladRo8fhv+CN3SAg7fVvwXPuZmsuiRJwqUo062bzWbYgnClnDZHWxrHioG2ZmM/bEArVqoUFF6ZBsPOub29vXApLS+FVV70lpRAAuSAzx0skOQo7Wh8nKOIYTMgjh1yoAAcJvGwRLF0TVRBPAuel+JP2bzVjQMKoAAADy//KpmzHoVHUSnm0wuiP78gksFgIHWNhOus7e3tMGdzbRf8/BxtCnej0ZBaurBJ6kqRZreYeuXC8ypNU9HK9dwzVgr7qtHv0e12O52OrJplPJH0nY3zLAJGtoAFciDJYAuPtJf3jl2cAt4DFlnPokRmo9iOVBDXxEzOAb/UDRdErjJCQZy+OiuIr/ae7txLZu+9nPFy2WdZdvPmTUkxYcIa1hVtPHuONgDpcbCG/QlXiyIEtVrNOSf3Xe7wJkceFkIO/mAwyLLsmWeemZmanWXZYDCI47gEYiCGRwnkzj06RJHmxThDMUKZAlk2XRE5jNORVQtxbYQBMjFq2Dp0k5gTRA946h5fyhYXxCXAijQxAMO+UvJgpgXs6jhxjjYnnDy2TdY1KFHGzMvB6ff7og5RFIVm7CbXsSyEZAvkeR7ejUIHrvc+d/7eZJIBLkqRW+QZJsMsH2WwEdDLijgGSrhJmY7iEjZHroK4PqSZCqbRwM07QQMf4uwCWAQxm93gdBvw9KX008JbiFztUnySZRlXqeyzwmO7hoT20+ZoA+BosDiOZZs1WIhhi4Swu4QxRqJzUmF9BUpCw9k4RLqF80fKYr1ez/O8BFIgB+AsBj0MjlAmQBEhf8d3fef2zWeMaTdM+8b2wXvf830lXIFy6RekCuJZMO+aN23m0G4YpwiiB2CBDEjOJ4jl9N/5Tjhm4e7s7BwfH4sESJyKrCc6f9oc7XDJFkZ+17NLYVplr9dzzkm8LhzkdDVy/tnasixLCWeNRiOpm5TNjDGmVk+BSWl9MoGNkEe2//Cj/+c/NJ1t02zXrt0wpt0wrZZptGr19/2l78/hVBDXhDhxJF1g8xyIwOM48jRNwUmyQgEk038WJ1t8s7Ioamin/xY94cqy7Pf7d+7c2draYiCFKsNF02QykZVpWZZrs4Dm52hvb2/z+hQzbT0CLSviJEnC2wPTuUQlQ7v1shOORXTOyQkgPhP6lIuiKAHTaJlaEy6DHWH8aPzKbz9z55ZpNE2z8z/+wkd4Nx8eHr/tP/yG//Rd35OvwAm0gRf5BsHSMRr8my6IkNQtwFv4DIiAaEYQT82zmb5BORXE/FyC2Gw2m83maDTisjRN06Iowm71AMbj8dosstPmaLNWVzajdq8hqjuTVSOdbre2tsTHejUMQyIlSQi6WmDqRw7Hb7RaLVOrcznjoh5sD7b3nm/9MzVjTGvnZ37xo4cpSiBLUniXp5kFRtnyT6ANvMg3hbD7wMzoyI3hJEF0Dr6AT7LoEQWxdJm1llmK1LvcVUqX5zng4Etq4owg5lVu4xNyFnbeFzua/2/gPUM0N8wn3cD9lFkuWPYk6PXAsmV5LCMMww1mHshMG/oQsyyjD7EE4CKMX4I9/FfecFAzZvf2G1+4H1EQAeuKGHA5MM7VQlwjl0QQ3eySuXRwBVwCTGx6BESTcQ9AnldKl3oUU/+gtXZm4eyfFMTSAdNLVFJqeCpLswYAHIK+eUEneO9DowxAnudhL4nNwRgjIwBxkvdz82FaJT9FmqZ8IFO6pPrl+PiY4WZGVMSH6zxyIM4c7ADl/fEX/vGdjtlqtv/Q13xDBMTAMIqHoyMgA1w/RiblK8tDBfFULqUglkBp4bJHL34WfuSzw//2Jz54+9Y1Y0y3e/PXPvHPMqCfIQNyoPCBJnpRxieWzLasKjroBJwpnpsxDDczkThcGo9Go06ns5ltSlutlmS/buaRPIPwkPIOxJmIsrAQ1WO6pfQNQ9DTyAM5MJ5kcAO4V+5+6iO3mqbd2v6Tb//2CDjMkJQlkAFxlEwSr4K4XjZfEP28IFrAWpQJ3ARuVIzvff3X/uGtljGmbkz7B374b8VAzyIGMiDKna9MJylNYeno47jKcDRBMLWd/08mEwZDm80mj8zGdoQM45uj0agsy4ODgw0siUvTVNyI9CFaay+dhcjypJn7Df0qXGRwuhZT9MNvoTIhuS7JAddD+cXxF37lX3qu3Wps/zv//tvpDreA9RMg8rBHE8SlCuIauZSCWDqUBcoIbpT0fqd//3Nv+F37DWO+8RvfUa/vmNb1Fw7zETDmAiR1ZWXl0UIspFbPB2k3o9FoJuIpnjiuoJldiM07PiEMIjPdbzP3M0zYvOh9OQ9S8IPpSuLll18Om3rI7TM8ndgxF8Arr7ziAVsVXB2j95sYfPLf/FefqZnm7/s3/ujnH+AwZZQvGo3vetgUmFgVxDVyGQSx0sTqBwqizSiI8IOf/PG/2jTmT33tH/vMZz67s3PD1K/9+P/0kT4wACJgkKHk2ektfAFfhPXLPDPDljNHR0e8z/PMnik42VgjkapNI3fzao0qHj169MY3vhHTFeXGHszTmOngG3Y2QlCUws810y9KmsiWDpadbdwhst9C+bm3v/Vfr5lmc+fLfvkfvfQwhgUKPwBGpc+H+TQCs1RUEE/l8gli6VBa2Aw2QvQA9uhPf82/tWXM//rzf+/4uN9q7Zmtm1/9J/6jeyX6wBgYl7D8UJUgZpUmBtnaYv2JV0tObp7EaZoud3LxcgmNEWPMaDSaSbjZHGQIKjk+Pr50piLXy1Q6Ds/hApmt3sKEBIl00T9A+z1ObJKz1dcj+BfgXvjwz/yNf/l3/15jbhvzpR/7jd+xcKk9Bkbve/97/9Af/7PjQgVxjWy+IOJxnqCDd3AWZYEyQRmhnPzqR37u1m5ty5hP/sYnAPfud/8Xpn3N7L/xt8eVIE6mkZOqzo9G4uOFc5Wbw3OXi6Cw1KzT6YR7soZ20+eD+xzHcbvdnk8H2RxkyTzfo3/z4f1S7pplWW5tbRljwnsPl88zn0vyVcG0Bwd4lJO78K9g/Dxc769/8G+a+u36zptM7cDUzfaOMXVjauZtf/Y7M03MXieXQuNVSWcAAB+GSURBVBCnmdYORQIk8BHsCG6CMnr/n3/XljFf9ZX/Wjo+LvPhx3/9I6ZhTGP/x//nj9KN2LcYlcirdYe0xike9/7y7owzLssyNkamYsqpL51f2VecYQ25VMIuk+uJpZZlGUXRjRs3NlayiRTLi2pfoHAvJa/wHH93+gekzqrgk8+94V8wpmVqxtRMZ6f1gQ/8QLECByJUEM/gEgiiRJZZmlKOouHdaHgPSHwef8mdmy1jfuAv/gX4DH7sike/60sOTPv6f/AN3zEG7o5dDKRAP8kmeVpWwRkLTNXQWbhTBVEUjT1fjTHD4VCWS/Owevfu3burOxgnIovQsEHpZjay3yhBJK8xr3C5+y+3T5noHRa6LAsVxFO5FILosnJaq5cCETABIiD7lY/+ctOYna1Wwxj+u3OrbWrG1LumfuPXP/079ydlCmRAP8ksUFa+SGkQ6yo1PPOUDhtqdbvddru9u7srCWjD4TCs05KxbRIxWM+gu8lkEsfx9vZ2HMeSp72BbJQgLiWvcIlwQvQalhQqiKdyCQQR0+LlModLfDkEJkBSpMPv/Z537XV2GqbeqtWv7+3eur7bqJl6w7T375idO+967w+m01ZLBTBJsxLwYcnK07UAm7ls6Pyaaf/JaUT0nYv9SLlcxfE4EXYqksuJ0rxpbJQgkteYV7iK/eHpFMfxigocVRBP5RIJok0jNvsqsmMgsdnkK970xht717/7O/8c9S2LJkA2iQad/Rum3v3Kr/6DOdCLMy6Sc+dnm309hRq+8sorAETsyOHhIYAoiuheDJtZ8SWxKDmpcpmH4iTYakUEen74+uawaYL42vMKl7gz8/K3ootRBfFULoUgJlEKD7hi2v0wQRn/5N/+iYYxDdP8zCefR4lp6bJ1zv7gX/kRU2s3tnf/8W9+2gIlMIqTsPvhYyU8UxBlYJ5cM2L9jcdjOX13dnZEjEL54wW2ntWr9OsW4d7MLL+NEsSl5BUu8Xrhn/Dej8djVnmv6OCoIJ7KpRDEPC3YDjZJ+klyDCT37730zv/kP241tr7y9/8BODy6P0ojB49Brw/gwx/5ZdPYMrXmX/rAX6ECJmluSy+aOCOOpxGmj0lrv5nBUjJPWa4faqJ0hF6DICZJIjnkG5uBSDZKEMlrzCu8jH3MVBBP5VIIoi/hbJnEIw4MSJI+UEzGQwagiwQoAQdXAB5pnGAqcx6I4rR08IDzT3TJnpHFMwhH94ZYayVVW5aozMaQTjPrSYLhFxfmjW9s34SNEsSl5BUul3AeTnhtLhcVxFPhFZum6WAwuH79+obe7ipDLpygUlRRETdVNSeNYzHTETZ8jxlNtK9hhMA8Yb6LMabVaklbF15CNB7DgyzZHvzxbD89rw1ZqkuEZ6FB6Wsg/BThcGpjTKg+EsNdFheVV3jpUEE8GXqUxYqJoujatWubmLGxsCBOxzg+hSYuURDxpKeJl9lM3zCxj3wwy1QIu8/PI98UxY4V1vV6nWooxsWGZCDKmC0Sx3G3283zPIqiULaWbgFtVF7hZqKCeDJyXsZxzEj/BrZZBkJXnw3mjk7zZp6QQgSzUp4URA88nub8lCk3C+6m92KXMXNNfBHNZnM8HvNSDOe+jsdj0dCnGcBC7fPeM6vGWsuvbGZtPr/KWyes3pHHnOOOuaFXS/cnbFpe4caykRf5BuCckyWzzFTZxFXzaYKIeWEL59YHghhsNieFS44SjsdjmeVEVaI67O/vdzqdGUftvDV3toWe57ksM6Moun37trVWIp7s1sNXLza0MplMiqKQ5tjcQ1Gf8Bxb+tyrTcsr3EBUEM9C0tbu3r27kWNIQ/VyOHEy/cmvniyIU9yTtuRymOm2zfwJTA0Qyh+vRky17+joiAbdqzrpJZOGD/I8N8aIJSg2zkw2yYUgvrlw97a2tp5//nnZhsdquUvUjcor3FhUEE9Grl45h4qi2MRV8xmCiFDjwmp5O79enhPEaaOHJQkiDZ80TXmxyZIwDB3Qq8VEGR7qsL5FrKrTiOOYq2Z+ZbyBUR8lBTIciHwhyIJDPssLL7wQ+lJXlKG5aXmFG8vmXeGbRJhjzP5RF7s/J3CWDSg4jgwAIo/Cw3q42QTsxz9Pu2eHq+9lIBckBUvuNPQVlmUph5r6xas0HGR8xptHUSSDAJMk6Xa7rO6Sa5jPb87SL0kSUZz9/X2ZyhBusHQBeh3mFS6KCuLJWGvlfJXRzLVa7UJ36iSeEEQ7VcN5QawsRI8iVMOTBTFsBbY8QcTU7pbAggQ6xfrLskxCLrwymf4WjqM762BMDZ/Qlg+bfoe7cVGIGYhpUtFMw935HV7KHwU2K69wM1FBPJnTBpzzsZw0YY7bBhB0Zzjhpaf3CZ7xPutDLMo4jo0x165dO/sCpmhKPsBm5s2F+StJkjDH+ByuGM0rXBEqiGchgU6eTKPRqNvtsh2biOC9e/cubP+uLrSSsizj9SxfxGlLPIZKuc3u7u7S47PLoiiKsizDAPrW1ta5303zCpeOCuLJzI8J5yXaaDTklitX3eZ4pq4YvA9JkUmSJKcFASSpW6ytLMvW029xIeSkolSdO79V8wpXhAriycjS7OjoiI/Z2YWnb5iscOFpHFeVmeRk/nhGmghzpGg/SrnrpsFGp+HU1u3t7XO/m+YVLh0VxFORTIWwLzSedNgnSbKZ3UYvO6J6x8fH3vswAnviBc8vhZ0jZBG9Mb7dWSRDiDXd57unal7hKlBBPBVrrVxRXHxxgWaMEX+NsiJ4hc8oWqgdM0tC7/3u7q4xJmxDu4F2UBRF4YcK0y0XQvMKV4QK4lmwq6icwTyBkiRptVoAoiji1bghLQOuHv1+n5d6nueibicGDcqyPD4+bjabzz333Cbmzz8Jiwhf+35qXuHS2fRT56KQTDFZbvC0C0vxpfLsYnbxSpOmKe9DvJJDQSTzaSVhD9qZuS4bSK/XY57/+ZIiNa9wRWz0SbOZDIfD7e1tubtu4LrsajMf3KcmhgoYrhybzaaUwYTqEE4EBCAD+VadyE0Vy/O80+nwLGI7Jc0r3ARUEBdDQihStXKxZQ+vN6hrkk9TlmWapt57UUNOlQr9a4PBoNvtdrvdcLCvVM6J6tHdtupSP+lyxlJr7334JzSv8MJRQTwPkn/Dq0hXzWsjjG4h8IJ1Oh2OXcZUDRmE5ZYcBs0OY+ENTFblM/OnVtcMgnpnrb1+/brcXMO+sNC8wgtFBXEx2MCOjzfcS3W1GQwGbCwoydiy/JRGD4SaIg21aFVJUxkGH6gpoj4rbRfGZEk+jqIodOdpXuGFo5f0eeDIjk6nE0WRrlPWzGQymcka6XQ6tJ7E0KNJaK2l8NG/FiYzGmO2trZmpv3SkbfShrLczzD+g6mcaV7hJqCCuBjhRUU30MaWzV5VqHqiVmEzwbALN+bSGGeS9QC0221GJChAXC+vdOSAtLcJp2L1+33NK9wQVBAXhjd22ik3btwI87eVVUPjiImf1lp+BVQZPinfjrQaQzCeRUzIoigoOvxfBhiseihVGP/haXP37l15VfMKLxwVxIXheRwmJOqqeW3IoU6ShNc/vwJ+KWGRpajDjBMw7Dgr9TCykl312FLnXLvdpr+Su8o2IppXuCGoIJ4H8f6kaSrF+bQmZO1DV/1F7eEVRlSDQx2Wezdi/gADuNKQhi/NP8C0ta2U0/C3vPccpopgdIxUpwwGA9Fo/okww1/zCi8WFcTFkMYqmForDBrKY27G3AhlRcRxLM41SaheImmaNhoNFkfzu2aKDMUOc4OVGZUOhVJelV6wOCktQVzSmle4IaggLgYNQOccr5A8z3mTbzQam9mA74rB+D6AKIqazeYqJOP4+Jh6RF/e/v4+hYw3OXE+cmdkERCKcq/XCxt8URyZyc/tw2oT9s3WvMINQQVxYSQ34tGjR5heFXLzH4/HvO1rW7BVELaxaTQazKleonzMhJjv3bvHESjGmFarRaGkfSor9+PjY7oavfeSMY4nU1YfPHjQ7Xbn56kmSfLmN79Z8wo3BxXExUiSpCxLsQRF9WRIKc2HmetKWRacU1qWJXOeKBzL9dUOh8NQj6QXNwBWRsvz4SQJQscxa+wo07w77u3tYWoY8tzgtNVGoyH5Q0TzCi8WFcSFkcow+ZFVVoPBoNFoJEnCa2Am6VdZIt77ZrMpa+cl+hBp4kVRJBNo8zyXQJk0xAzbHTnnmPUyGo1CEZREGTbQDDNjaG/yL4rNqHmFm4AK4nmgYRi2SiTibOL1o5q4dDg+RfRo6UdYgiGyNg/7MGI694rB6Fartbu7K8tkbkk1DDN1xJ3C37pz5w6lPKyr0bzCDUEFcTHCk1geSCLbZDKRs39m7riyLCiIYfLNct9fTDbOUxSvCBMGwzCOtTZNUwaj+Qw1UYr/QueyLLfDjHESWoKaV3ixqCAuB/q2+NgYI40GZCK7XEgaiX4aJD7LIym3H6rJ3t6eTNpbjxl+dr9Cmn7SEU721hjjnGMZjObQXApUEJcGnU087/f398VZLlfsvXv3eCHpUuhVEfUpy5LONbmRGGNkWUrdXFtMdr5fIb9cEbvt7W1jDLs0GmPEeAzDKcomo4K4HBhw5HkfxzG7wwvj8Vjc7Vr4/DTIHNHw5sERK1x4clHJljZr2J/T+hViqtRsyi1RlEaj0Ww2RQGlH62y4aggLoeweEucR3Q5sT0fW90haNOivCpSsHx4eEh93NnZ6fV6F9Wl/MR+hUxHxVQo6/U6m+jQ54igRY2O8N58VBCXAwuZh8Mh44Nh6wdCN6I6kp4SHs/5el5p5cDclCiKpMP+qjmxXyF/ZCUf18hhPxs8mcaobD4qiEsjXBNJJxVjDBs7I0iq0MvjKaFP9uHDh9THMLhM1nYkT+tXWJblaDRqtVo7OzsI0gyOjo6kdZgEkTUNa/NRQVwOdCQ9fPgwSRLOShdarRYdXrJY1qXT0yB5zvLj/v4+pg1mJF9aRi+tgfl+hc1ms16vs3gGQLvdLopChE/ukS+99NJ69lB5jaggLoeZ8WnUR1nNSdMUhkdVEF+V0BLM87woina7nabpfAnHetpkndavMM9zcR+HK2VpGyzlfWFeqg/+wQM4sSLFnfK8skJUEFeLJOLw4gEwmUzCBvHSPSXMdFNIOA9vuSO9Fp2DHA4+rdfr9Xqd9qms2Wdys0/DA0mal4AFcsAC8A5lBriyLOFLwBXWWWvhC/hCNXHNqCCuHJE8SdyV5+XxYDDQwtWQmb4J7Dez9L/y9HOQAYzH42az2Wq1er1eKJd5nm9tbQEYDoev+iU6D+dBQUyB3KPMYp/HacJpZQ6+TLMCAHwBG6sgrhkVxNUiq2OmrTEbA8BkMpHWeNI7T2PQIdJra2Y1uhQWnYNsjGFuqZiEeZ7TWczeDXxyZiTLiXigdJikRWJReMBbsQSLophMJh6wpR8eP4K3KohrRgVx5VhrwwXXzIyhLMtm6tIUQQwujgxd+vF5+jnI/I5o7IdmIIvz5Edr7dk+TXoAKLseyPN8Mh6Ohv3RaFQt2/l8UWoC/4WggrhapBUK8xOpjOwftdCF9HojjmOqhnNuZorxslhoDrIYfaHT8JlnnsHCNzYHb7NoVBmGNgPDKkAURc7DA48Ojz1ggQdHfV0yrBkVxJUjU9xm0tAWXWq93pAWWBzj5b1fYvXbonOQucHDhw+5GV8dDAYLuj4cbOHyJI+GcAns+PCVL5RADkyiJM/zOK/2Kc2KR+M8AzQdYc2oIK6cJElC6yZNU3rlF3LGv95gzmaWZVtbWxSpVfgTnn4OMoIhfDOzZxcJjjl4B1/AZygnf/evvf/Nz15r7eybene7s7e3t1drbX/9276xd3zogaMMsQri2lFBXC1i9MVx7JyTq3rRdI3XIbSaeXzoeltiAvaic5BF/sTXERqYT58+VdrcJmO4BMXgB7/rG7vGmM6B2bppak1jjGl1TK15+/r+hz70oQgYMC9HWSMqiBeGTONtNpucEGKtlXovuVZloqksGOWivQJBmPk7RLgulrvFq8bfJUVGMmacc0VRMKtG0uZFrShntBAbjcZMFNtaS/+GuDLPaAS7IA6+gI1gex/49j91YIzZu/Nbxy73yLLs//6nnzK15pYxnVb9b/70L/QBvUmuGRXEi4EOMsmAC1src8gRS9P4jDQW4+MkSa6YOZnneTiPgX0G4zjudrvyfGhfnwHnI5/tjZXc+Hq9zluRpH+H3cbC5tWnjQo4D97CRrDHP/xtf/ymMWbvuc/0KkswLvyLL738lmevNY35ff/e1336YXGlvubLgAriRSKhSV514ssnvP7pyOfVKL7IoiiuTARGqtww/YD8sOFcvdFodLY5JnY0gsWsDALNsmw4HEq+4e7uLn2FtEZ5c8K0xY4Y6Rya3O12pcnricOkFsIDgIONYA8/+K1vvWOM2X/Dp/q0BF1ceADveefb2sY07rzlCwk082DNqCBeDLzqQkNPWj8YY+TylrAmkRHmV6m5nnyW0LJjNy0eHzHNwqnHJzIcDqUFIctLaDDKBnLLEQmWsbHhyHkxRRn1wtzkFhk3utAn9UBJTSwT2MO/8S1/5BljzLUv/80BJgUAZ4Gjo6MP//Tf2jPGdJ798KfvqyCuGRXEC8N7TxtEYgUS0Nzb2+NccwDsRy+jKa21Ip1XwEiUj3B0dMTHLE2x1t6+fVuEaT59egYezJlcTlGx0WhkjKnX63xDVpiEliCm+dhym6nVajJDkc+cNpD+6fFAzsBxmcEe/tff8gefNcYcvOWfDJEB8NYCtsj+lx//wes1Y3a/5Gc//nkVxDWjgngxnJhmLAZgHMf9fr/dboeLspksPAmAXmqkrbTAjykB3+PjY25w9vpURiHzQb/fF8PQGMNmhQDiOJ458jIAQPYHc40kQgdFaJiH6/SnoQQyBo7LDMXDH33nv/usMebgX/zECBkAVyS590X6S3/7A9eMMVu3f/Wl+NJ/wZcNFcQL45VXXsG0XqIsSxodkuXLbbjEs9bOZG6LdXM1mDHWRqNRvV7HtDu/BDrOTszmIRJDcjgcSlyYQRvZkoEpPpbt+ebs/i9b3r17N/wTvGOdO2m0ZEMHVIL4Y+/8t58zxhz8no+PETkARQkko97f+f7vuG6MOXjTRz8/VEFcMyqIF4OYP+GTNE/EFArnzO3t7UnFC6betEs1vc8F/x7Dj8CPI30D9/b2AERRJObYzHC7ebiBqBu7+dMXEWZWh06G0L52zlEK2f8GQaSFv8VAfzg5Jxwt+5SwIG+6ZD7+4Le+9dbUh5h6wNsSuHf35QNjusZ83Td/9xE0qLJuVBAvDWGKMgIHWejvp/HCy565Owhy7tbQWdrDPdH69PEPFiiADCgAFzwPBJENWbEumleIqZlJm1pC0mEzBSGMh5y4Rl4ZDt4mg0c+7qOcfPc3fd21urn57Jf+8xcflsBgOP5nn3ne1Fq3bt1qd/d/8Vf/6dBrYva6UUG8NDx8+LDdbm9vb4f1FfPDmEQgRBC992LvrBoPV84IohNBzICkcqNNBdH7x1PrqOYz2vSUeYWYDv9EECSZH3CY5zmtcqkquXXrlvzF86cWPiXewiVwEVyEfPz93/c93a16w5g7d241m1vN7a6ptczWrql3PvQ//FwKaC3z+lFBvBxwUSm9+Wb65YRmVBzH8/EWaugaKlt81QL1SQsRmBVEPGEhZllGezBN0xs3bkwmk0XzCilqoq2htDFmzehNuKYm0sZ8RQfkSZxLhsjHcEkyePRT/82P7rRqDWO2tprG1E2taWqtt37dN+RABjwYpv3YarebNaOCeGkIhz7zR8kZ5tQRWQaK83E0GnnvxVO5+ga0zsOeIohuumR+QhCTJJOPVpZlq9UK40VPn1eI6ZI5jmMenyiKuHBO01Sm2oe/QvtRFtdlWa4+au9QJPAZfIYygy9sGgFVZPzR4TE7afcn6f3eJAeKx7cMZU2oIF4awtiojHnLsoxFF51Oh+ahyN+M1bMWI4iqFxiAJwjiExtk2RMl22Hx8kJ5hdKCgYeISYWyMQKTENMbA+uUOSVqXXP7HLz1eQxfjHqHvkgZZWJajwfiJCtRDRgYJUWUqYW4blQQLwe88nmRiwEosQg+ljb3SZIkSRKGbteVwk3Vm45GmtVEO311dslcvWyt9ENbNK8w7CokP/Z6PSZ4S5hlNBrxcNEmlRsM7y5L70F7Ei6ajKiD3tloMrp//z5fSJKkdEjS3AOHR700K1QN148K4qWhLMuwnvfevXt8QOuGijkcDudXkdLab/VGonu8KA7CJtOH1qPwc4Iofr1WqxXK90J5hQB6vR43Fl2j7SybyWL86OgoyzJu1u/3xQWxqqNyEoPBQHyjk8kk/GpkrveVqc68RKggXhp4eRwfH0tJH5+XEZrVpI7p1NNr166FCShruboskAAJUISCyGVgWXkYbWg/5rnF1J03s57FInmFIiiHh4c0Cedn1/DHMBVJJknxz63hEBXWeYCjAjCNAvEjT+s4Y8C5srBFphOm1o8K4tWEyXplWW5vb1MdpFC3LEsaR5KXE7Yak5Upr1J/CtxMBKuy5rIIiOAj2NTlBRwG/aQsK0G8f3xYwvbGxx7OecRRTlXg73Y6HRlzLPuJJ8MmbGQdfsYwlESvIktcsL7A8WJ4yO1h3meAKnHdO3irI/cuBBXEK4s01KHK0MPIngU3btwIkxm5ARWEAw+exvM4Ho/DdetkMgEsimE+ug+fwTube5qHucc4LSxQwpVwSZYyDp0mj9/fTCfbhc+ELaxpHopWZlnGIVBhtEQKk0/Mx94Enk4QrQriRaGCeJWRHjmY6p20jTHGsGm+CaYpYa7P1WmEXbvlscuTn/rQX7uza27ttZvG1EzTmLapd02j85v/72dzIPPlIBqW3nnAO5QF8txGUcQxUuwDxh+5V6GVR0FsNptbW1vcc0wNWG4QhkToUd1MQZz59yRu7p+yVlQQrybWWkklmUwmlLm7d+9KQ3y+JI1pGX8wxnBLeirPthBZ9stuXdPnivd/73dsG9Otmy1j9roHxrT3rz9nGp2f/8j/ngMWyGFpHI0GETyKoloX8+82m829vT3RcT7JHbt+/Xq73Z5pbc0ETD7DWETYlmYtUeOFWUQQlXWjgnjFkfIM5ieGy9Kwl0yWZXTPccDI9evXW61WvV63pxC681hQPBwOyzx637vfuWPMcwftL37ut7hkjjLkAKsvqImjOEmzAh55WqkhAFqFzMRmWiV9grVajX+FMQc8mWNIJOgsFqV0D1KUhVBBvJqkacp0XzawoppQGaMokuTtMIlPFtfiHCzLsnEKTAak7cbkwclkAhTv+c533Gyb5w7aLz3/WYaYJylyYFRgkBemUTd1U2ttdXf3jWntdQ+MqV+7do32abvdDhNlRNGOj4/FCA0rVXq9HnWcz4jiyy9upIX4VNbfKfajsnJUEK84URSFnR3CfgdUPZaIUE1CB6KMdjoRbsMFeJIkxpibN282jOka0zXmoGF2m7XKh2i6pr5jOvtmq50D4ywpgdE4Go9SueLH4zEX79y90WjEfWZdNrcRM5DNuGZ8naH6bzZhBHlWGUUHJeqirBkVxKsJc1nEVyjpNZi22hahCcezcCkqjf/ORtx8UkQIZO/9rj/zxmtmx5iduqmZdq1x0Oo+8+73/dCoQAbc7T2003Y4bIzD0r0TR9HLzvP5+bas/BTs5SX6yN/i/j9lgGi9OMDCn+woDAVRLcQLQQVRWSLJD7z7HQfG7BjTNKZm9o25aczN7/v+/yoHJnka25FH5mF5zaev0+4F7lU/9evxqGwGKojKEkn+4n/2pw+MeaZreg8elR69CTJfhVNKOI8EiDIbVbl4Xq98ZbNQQVSWSPLub/maG3Xz3EHz8P6D+w/TzCPz6EWYFChgPTIg8SgoiMWrm0qKslZUEJUlknzwfd+yb8zBlrn/8iulR+5xOKo6IFqUaTZkpbODjzONGygbhwqisjx89u5v+5O3t8yX3ur8zm9/ofQYRMiAFIhyV8IBWZIObJmW3uWlCqKycaggKksk+6G/8O1dY7aMuXPrtjFdY/a3r73JmN2f/fu/MIkjoMiyYV7EElRRQVQ2ChVEZYkUP/ljP7RjTNuYZr1hTKfRuW3Mfm37xk//zM/1hwPAujIFrAdyh6RwKojKRqGCqCyRAuUYbpRH/TRNLTDKkANZiZwZgd5l0QhwRWmHUaxLZmXTUEFUloe3cBH8BL4AnEVVxWwfz5xykpOsxRjKBqKCqCwRB5/BJ0DhnxTEakCzA1yliaWUrCjKxqCCqCwRFuoWgBVBtJy27oNatceCqD5EZbNQQVSWh3/CAJwVRI7XdDQLXQlbwnrt+qdsEiqIyvKQwVKVILocrnIguqkgVj/bEkWJQgVR2ShUEJWlUgkiLJyFzWGrdbGbjmVWQVQ2GBVEZaksIIhZiUwFUdkoVBCVpTIVxBLOwlrYkpInS+YqtGy9WojK5qGCqKwED3g4L3Hk2dFKDnCqhsqmoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpSoYKoKIpS8f8DBf2iO+zA8l8AAAAASUVORK5CYII=" alt="" /></div>

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CBSE - IX - Mathematics - Circles

Two equal circles intersect in P and Q. A straight line through P meets the circles in A and B. Prove that QA=QB. 

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CBSE - IX - Mathematics - Circles

In the figure, two circles intersect at B and C. Through B two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively. Prove that ACP = DCQ.

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CBSE - IX - Mathematics - Circles

In the given figure, O is the centre of the circle. If OAC = 35o and OBC = 40o, find the value of x.

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CBSE - IX - Mathematics - Circles

Prove that the angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

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CBSE - IX - Mathematics - Circles

O is the circumcentre of the ABC and D is the mid point of the base BC. Prove that BOD = A.

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CBSE - IX - Mathematics - Circles

In figure, O is the centre of circle. Calculate APC and AOC.

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CBSE - IX - Mathematics - Circles

In circle having centre 'O' find BAC

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CBSE - IX - Mathematics - Circles

In the figure, O is the centre of the circle and BAC = 60o. Find the value of x.

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CBSE - IX - Mathematics - Circles

In the figure, PQ is a diameter of the circle and XY is chord equal to the radius of the circle. PX and QY when extended intersect at point E. Prove that PEQ = 60o

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CBSE - IX - Mathematics - Circles

In the figure, ABC = 45o, Prove that OA OC.

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CBSE - IX - Mathematics - Circles

A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.

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CBSE - IX - Mathematics - Circles

In the figure, chord AB of circle with centre O, is produced to C such that BC = OB. CO is joined and produced to meet the circle in D. If ACD = y and AOD = x, show that x = 3y.

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CBSE - IX - Mathematics - Circles

Two circles intersect at two points A and B. AD and AC respectively are diameters to the two circles. Prove that B lies on the line segment DC.

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CBSE - IX - Mathematics - Circles

In the given figure, AB is a side of a regular hexagon and AC is a side of a regular octagon inscribed in a circle with centre O. Calculate angles AOB and AOC.

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CBSE - IX - Mathematics - Circles

In the given figure BD is the side of a regular hexagon, DC is a side of a regular pentagon and AD is a diameter. Calculate:

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CBSE - IX - Mathematics - Circles

In the given figure, AB = BC = CD and angle ABC is 132o. Calculate angle COD.

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CBSE - IX - Mathematics - Circles

In the figure, O is the centre of the circle and the length of the chord AB is twice the length of chord BC. If angle AOB = 108o, find angle BOC.

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CBSE - IX - Mathematics - Circles

The given figure shows a circle with centre O. Also PQ = QR = RS and angle PTS = 75o. Calculate: .

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CBSE - IX - Mathematics - Circles

In the given diagram, chord AB = Chord BC. What is the relation between angle AOB and angle BOC?

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CBSE - IX - Mathematics - Circles

A regular polygon is inscribed in a circle. If a side subtends an angle of 36o at the centre, find the number of sides of the polygon. Name the polygon.

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CBSE - IX - Mathematics - Circles

A regular pentagon is inscribed in a circle. What angle does each side subtend at the centre?

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CBSE - IX - Mathematics - Circles

Prove that equal chords of congruent circles subtend equal angles at their centres

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CBSE - IX - Mathematics - Circles

Prove that equal chords of a circle subtend equal angles at the centre.

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