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Equal sets of angles in a trapezium

Source: Pan African MO 2013 Q4

June 30, 2013
geometrytrapezoidparallelogramratiogeometry unsolved

Problem Statement

Let ABCDABCD be a convex quadrilateral with ABAB parallel to CDCD. Let PP and QQ be the midpoints of ACAC and BDBD, respectively. Prove that if ∠ABP=∠CBD\angle ABP=\angle CBD, then ∠BCQ=∠ACD\angle BCQ=\angle ACD.
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