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Source: Kyiv City MO 2022 Round 1, Problem 10.3

January 23, 2022
geometry

Problem Statement

Diagonals of a cyclic quadrilateral ABCDABCD intersect at point PP. The circumscribed circles of triangles APDAPD and BPCBPC intersect the line ABAB at points E,FE, F correspondingly. QQ and RR are the projections of PP onto the lines FC,DEFC, DE correspondingly. Show that AB∥QRAB \parallel QR.
(Proposed by Mykhailo Shtandenko)
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