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line connecting projections of intersections of tangents perpendicular to median

Source: 2004 Oral Moscow Geometry Olympiad grade 9 p4

October 27, 2020
geometryperpendicularprojections

Problem Statement

Triangle ABCABC is inscribed in a circle. Through points AA and BB tangents to this circle are drawn, which intersect at point PP. Points XX and YY are orthogonal projections of point PP onto lines ACAC and BCBC. Prove that line XYXY is perpendicular to the median of triangle ABCABC from vertex CC.
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