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A circle passing through a vertex and touching an altitude

Source: Indian IMOTC 2013, Team Selection Test 4, Problem 3

July 30, 2013
geometrycircumcircleangle bisectorperpendicular bisectorgeometry proposed

Problem Statement

In a triangle ABCABC, with AB≠BCAB \ne BC, EE is a point on the line ACAC such that BEBE is perpendicular to ACAC. A circle passing through AA and touching the line BEBE at a point P≠BP \ne B intersects the line ABAB for the second time at XX. Let QQ be a point on the line PBPB different from PP such that BQ=BPBQ = BP. Let YY be the point of intersection of the lines CPCP and AQAQ. Prove that the points C,X,Y,AC, X, Y, A are concyclic if and only if CXCX is perpendicular to ABAB.
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