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Source: Ukrainian Mathematical Olympiad 2024. Day 1, Problem 11.4

March 19, 2024
geometrycircumcircle

Problem Statement

Point XX is chosen inside a convex ABCDABCD so that ∠XBC=∠XAD,∠XCB=∠XDA\angle XBC = \angle XAD, \angle XCB = \angle XDA. Rays AB,DCAB, DC intersect at point OO, circumcircles of triangles BCO,ADOBCO, ADO intersect at point TT. Prove that line TXTX and the line through OO perpendicular to BCBC intersect on the circumcircle of △AOD\triangle AOD.
Proposed by Anton Trygub
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