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fixed point wanted, intersection of tangents to circle, perpendicular rays

Source: 2007 Oral Moscow Geometry Olympiad grades 10-11 p6

October 19, 2020
geometryfixedTangentsFixed point

Problem Statement

A circle and a point PP inside it are given. Two arbitrary perpendicular rays starting at point PP intersect the circle at points AA and BB. Point XX is the projection of point PP onto line AB,YAB, Y is the intersection point of tangents to the circle drawn through points AA and BB. Prove that all lines XYXY pass through the same point.
(A. Zaslavsky)
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