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A convex quadrilateral

Source: Lithuanian TST 2005

April 16, 2005
geometrygeometric transformationreflectiongeometry solved

Problem Statement

Let ABCDABCD be a convex quadrilateral, and write α=∠DAB\alpha=\angle DAB; β=∠ADB\beta=\angle ADB; γ=∠ACB\gamma=\angle ACB; δ=∠DBC\delta= \angle DBC; and ϵ=∠DBA\epsilon=\angle DBA. Assuming that α<π/2\alpha<\pi/2, β+γ=π/2\beta+\gamma=\pi /2, and δ+2ϵ=π\delta+2\epsilon=\pi, prove that (DB+BC)2=AD2+AC2(DB+BC)^2=AD^2+AC^2 [Moderator edit: Also discussed at http://www.mathlinks.ro/Forum/viewtopic.php?t=30569 .]
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