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fixed circle, all segments XY are tangent to same circle, projections

Source: 2007 Oral Moscow Geometry Olympiad grades 8-9 p6

October 18, 2020
geometryfixedtangent

Problem Statement

A point PP is fixed inside the circle. CC is an arbitrary point of the circle, ABAB is a chord passing through point BB and perpendicular to the segment BCBC. Points XX and YY are projections of point BB onto lines ACAC and BCBC. Prove that all line segments XYXY are tangent to the same circle.
(A. Zaslavsky)
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