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AB = AC if AP = AQ, circumcircle related

Source: 2013 Saudi Arabia GMO TST day II p1

July 31, 2020
geometrycircumcircleequal segments

Problem Statement

An acute triangle ABCABC is inscribed in circle ω\omega centered at OO. Line BOBO and side ACAC meet at B1B_1. Line COCO and side ABAB meet at C1C_1. Line B1C1B_1C_1 meets circle ω\omega at PP and QQ. If AP=AQAP = AQ, prove that AB=ACAB = AC.
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