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XQ passes through orthocenter

Source: Belarus TST 2024

July 17, 2024
geometry

Problem Statement

A right triangle ABCABC (∠A=90\angle A=90) is inscribed in a circle ω\omega. Tangent to ω\omega at AA intersects BCBC at PP, BB lies between PP and CC. Let MM be the midpoint of the minor arc ABAB. MPMP intersects ω\omega at QQ. Point XX lies on a ray PAPA such that ∠XCB=90\angle XCB=90. Prove that line XQXQ passes through the orthocenter of the triangle ABOABO Mayya Golitsyna
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