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Found problems: 1

2024 Yasinsky Geometry Olympiad, 1
Tags: geometry , right triangle , concyclic points
Let \( I \) and \( O \) be the incenter and circumcenter of the right triangle \( ABC \) (\( \angle C = 90^\circ \)), and let \( K \) be the tangency point of the incircle with \( AC \). Let \( P \) and \( Q \) be the points where the circumcircle of triangle \( AOK \) intersects \( OC \) and the circumcircle of triangle \( ABC \), respectively. Prove that points \( C, I, P, \) and \( Q \) are concyclic. [i]Proposed by Mykhailo Sydorenko[/i]