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collinear circumcenters - All-Russian MO 1999 Regional (R4) 10.2

Source:

September 25, 2024
geometrycollinear

Problem Statement

Given a circle ω\omega, a point AA lying inside ω\omega, and point BB (B≠AB \ne A). All possible triangles BXYBXY are considered, such that the points XX and YY lie on ω\omega and the chord XYXY passes through the point AA. Prove that the centers of the circumcircles of the triangles BXYBXY lie on the same straight line.
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