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a line and a fixed point

Source: tuymaada 2006 - problem 3

July 17, 2006
geometrygeometric transformationhomothetypower of a pointradical axisgeometry unsolved

Problem Statement

A line dd is given in the plane. Let B∈dB\in d and AA another point, not on dd, and such that ABAB is not perpendicular on dd. Let ω\omega be a variable circle touching dd at BB and letting AA outside, and XX and YY the points on ω\omega such that AXAX and AYAY are tangent to the circle. Prove that the line XYXY passes through a fixed point.
Proposed by F. Bakharev
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