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Polish MO 2022 P2

Source: Polish MO 2022 P2

February 12, 2022
geometrycircumcircleperpendicular

Problem Statement

Given a cyclic quadriteral ABCDABCD. The circumcenter lies in the quadriteral ABCDABCD. Diagonals ACAC and BDBD intersects at SS. Points PP and QQ are the midpoints of ADAD and BCBC. Let pp be a line perpendicular to ACAC through PP, qq perpendicular line to BDBD through QQ and ss perpendicular to CDCD through SS. Prove that p,q,sp,q,s intersects at one point.
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