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Nice problem

Source: IMO Shortlist 2000, G6

November 2, 2005
geometrycircumcircleperpendicular bisectorconvex quadrilateralIMO Shortlist

Problem Statement

Let ABCD ABCD be a convex quadrilateral. The perpendicular bisectors of its sides AB AB and CD CD meet at Y Y. Denote by X X a point inside the quadrilateral ABCD ABCD such that \measuredangle ADX \equal{} \measuredangle BCX < 90^{\circ} and \measuredangle DAX \equal{} \measuredangle CBX < 90^{\circ}. Show that \measuredangle AYB \equal{} 2\cdot\measuredangle ADX.
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