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Lines intersect on angle bisector

Source: Sharygin Finals 2022 9.4

August 1, 2022
geometryangle bisector

Problem Statement

Let ABCABC be an isosceles triangle with AB=ACAB = AC, PP be the midpoint of the minor arc ABAB of its circumcircle, and QQ be the midpoint of ACAC. A circumcircle of triangle APQAPQ centered at OO meets ABAB for the second time at point KK. Prove that lines POPO and KQKQ meet on the bisector of angle ABCABC.
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