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ABxAD=BPxDP+APxCP if <APB+<CP D=180^o, # (2011 NZOMC Camp Sel. S4)

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January 4, 2021
geometryparallelogram

Problem Statement

Let a point PP inside a parallelogram ABCDABCD be given such that ∠APB+∠CPD=180o\angle APB +\angle CPD = 180^o. Prove that AB⋅AD=BP⋅DP+AP⋅CPAB \cdot AD = BP \cdot DP + AP \cdot CP.
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