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RMO KV P-6

Source:

October 29, 2023
geometrycyclic quadrilateralcircumcircle

Problem Statement

The diagonals ACAC and BDBD of a cyclic quadrilateral ABCDABCD meet at PP. The point QQ is chosen on the segment BCBC so that PQPQ is perpendicular to ACAC. Prove that the line joining the centres of the circumcircles of triangles APDAPD and BQDBQD is parallel to ADAD.
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