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Geometry with circles and triangle

Source: 44th International Tournament of Towns, Senior A-Level P2, Spring 2023

April 4, 2023
geometry

Problem Statement

Perimeter of triangle ABCABC is 11. Circle ω\omega touches side BCBC, continuation of side ABAB at PP and continuation of side ACAC in QQ. Line through midpoints ABAB and ACAC intersects circumcircle of APQAPQ at XX and YY. Find length of XYXY.
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