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Hungary-Israel Binational 1991_2

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October 28, 2008
geometryinradiusperimeterperpendicular bisectorgeometry proposed

Problem Statement

The vertices of a square sheet of paper are A A, B B, C C, D D. The sheet is folded in a way that the point D D is mapped to the point D′ D' on the side BC BC. Let A′ A' be the image of A A after the folding, and let E E be the intersection point of AB AB and A′D′ A'D'. Let r r be the inradius of the triangle EBD′ EBD'. Prove that r\equal{}A'E.
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