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Geometry Mathley 11.2 AP = AQ , BM = BC = CN

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June 7, 2020
geometryequal segments

Problem Statement

Let ABCABC be a triangle inscribed in the circle (O)(O). Tangents at B,CB,C of the circles (O)(O) meet at TT . Let M,NM,N be the points on the rays BT,CTBT,CT respectively such that BM=BC=CNBM = BC = CN. The line through MM and NN intersects CA,ABCA,AB at E,FE, F respectively; BEBE meets CTCT at P,CFP, CF intersects BTBT at QQ. Prove that AP=AQAP = AQ.
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