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Prove quadrilateral is kite

Source: Canada 2000

March 4, 2006
geometrygeometric transformationreflectioncircumcircletrigonometryperpendicular bisectorgeometry unsolved

Problem Statement

Let ABCDABCD be a convex quadrilateral with ∠CBD=2∠ADB\angle CBD = 2 \angle ADB, ∠ABD=2∠CDB\angle ABD = 2 \angle CDB and AB=CBAB = CB. Prove that AD=CDAD = CD.
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