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Equal segments, circle tangent to sides of triangle

Source: Tuymaada 2018 Junior League/Problem 2

July 20, 2018
circlestangentgeometry

Problem Statement

A circle touches the side ABAB of the triangle ABCABC at AA, touches the side BCBC at PP and intersects the side ACAC at QQ. The line symmetrical to PQPQ with respect to ACAC meets the line APAP at XX. Prove that PC=CXPC=CX.
Proposed by S. Berlov
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