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Circumcenter lies on angle bisector

Source: 2023 Austrian Federal Competition For Advanced Students, Part 1 p2

May 4, 2023
geometryangle bisector

Problem Statement

Given is a triangle ABCABC. The points P,QP, Q lie on the extensions of BCBC beyond B,CB, C, respectively, such that BP=BABP=BA and CQ=CACQ=CA. Prove that the circumcenter of triangle APQAPQ lies on the angle bisector of ∠BAC\angle BAC.
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