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Geometry, XYPQ concyclic

Source: KMO 2023 P6

November 4, 2023
geometrycircumcircle

Problem Statement

Let Ω\Omega and OO be the circumcircle and the circumcenter of an acute triangle ABCABC (AB‾<AC‾)(\overline{AB} < \overline{AC}). Define D,E(≠A)D,E(\neq A) be the points such that ray AOAO intersects BCBC and Ω\Omega. Let the line passing through DD and perpendicular to ABAB intersects ACAC at PP and define QQ similarly. Tangents to Ω\Omega on A,EA,E intersects BCBC at X,YX,Y. Prove that X,Y,P,QX,Y,P,Q lie on a circle.
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