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Tangential quad

Source: 239 School Open MO, 2023, Junior league, Problem 3

March 30, 2023
geometry

Problem Statement

In quadrilateral ABCDABCD, a circle ω\omega is inscribed. A point KK is chosen on diagonal ACAC. Segment BKBK intersects ω\omega at a unique point XX, and segment DKDK intersects ω\omega at a unique point YY. It turns out that XYXY is the diameter of ω\omega. Prove that it is perpendicular to ACAC.
Proposed by Tseren Frantsuzov
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