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Iran geometry

Source: Iran MO 3rd round 2017 mid-terms - Geometry P2

August 10, 2017
geometrytrapezoidAngle Chasing

Problem Statement

Let ABCDABCD be a trapezoid (AB<CD,AB∥CDAB<CD,AB\parallel CD) and P≡AD∩BCP\equiv AD\cap BC. Suppose that QQ be a point inside ABCDABCD such that ∠QAB=∠QDC=90−∠BQC\angle QAB=\angle QDC=90-\angle BQC. Prove that ∠PQA=2∠QCD\angle PQA=2\angle QCD.
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