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PQ is perpendicular to line passing through circumcenters

Source: Sharygin Finals 2022 9.6

August 1, 2022
geometrycircumcircle

Problem Statement

Lateral sidelines ABAB and CDCD of a trapezoid ABCDABCD (AD>BCAD >BC) meet at point PP. Let QQ be a point of segment ADAD such that BQ=CQBQ = CQ. Prove that the line passing through the circumcenters of triangles AQCAQC and BQDBQD is perpendicular to PQPQ.
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