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AP is perpendicular to BQ

Source: Baltic Way 2009

November 27, 2010
geometrygeometric transformationreflectiongeometry proposed

Problem Statement

In a quadrilateral ABCDABCD we have AB∣∣CDAB||CD and AB=2CDAB=2CD. A line ℓ\ell is perpendicular to CDCD and contains the point CC. The circle with centre DD and radius DADA intersects the line ℓ\ell at points PP and QQ. Prove that AP⊥BQAP\perp BQ.
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