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perpendicularity related to a rectangle and a random point

Source: 2007 Sharygin Geometry Olympiad Correspondence Round P12

April 26, 2019
geometryrectangleperpendicular

Problem Statement

A rectangle ABCDABCD and a point PP are given. Lines passing through AA and BB and perpendicular to PCPC and PDPD respectively, meet at a point QQ. Prove that PQ⊥ABPQ \perp AB.
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