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Circle passing through the midpoint of BC

Source: Kürschák competition 2019 P1

March 2, 2020
geometrygeometric transformationreflectioncircumcircle

Problem Statement

In an acute triangle △ABC\bigtriangleup ABC, AB<AC<BCAB<AC<BC, and A1,B1,C1A_1,B_1,C_1 are the projections of A,B,CA,B,C to the corresponding sides. Let the reflection of B1B_1 wrt CC1CC_1 be QQ, and the reflection of C1C_1 wrt BB1BB_1 be PP. Prove that the circumcirle of A1PQA_1PQ passes through the midpoint of BCBC.
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