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Proving a tangency with square, incircle and parallels.

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October 28, 2010
geometryanalytic geometrygeometry unsolved

Problem Statement

A circle touches the sides AB,BC,CD,DAAB,BC, CD,DA of a square at points K,L,M,NK,L,M,N respectively, and BU,KVBU, KV are parallel lines such that UU is on DMDM and VV on DNDN. Prove that UVUV touches the circle.
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