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equal angles from an interior point of parallelogram

Source: Czech and Slovak Match 1998 P1

October 1, 2017
parallelogramequal anglesgeometry

Problem Statement

Let PP be an interior point of the parallelogram ABCDABCD. Prove that ∠APB+∠CPD=180∘\angle APB+ \angle CPD = 180^\circ if and only if ∠PDC=∠PBC\angle PDC = \angle PBC.
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