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Equality of angles in trapezoid

Source: XIII Polish Junior MO 2018 Second Round - Problem 4

April 24, 2018
geometrytrapezoidPlane GeometryPoland

Problem Statement

Let ABCDABCD be a trapezoid with bases ABAB and CDCD. Points PP and QQ lie on diagonals ACAC and BDBD, respectively and ∠APD=∠BQC\angle APD = \angle BQC. Prove that ∠AQD=∠BPC\angle AQD = \angle BPC.
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