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A geometry problem

Source:

June 9, 2012
geometrytrigonometrygeometry unsolved

Problem Statement

Let ABCABC be an isosceles triangle with AB=ACAB=AC. Let DD be a point on the segment BCBC such that BD=2DCBD=2DC. Let PP be a point on the segment ADAD such that ∠BAC=∠BPD\angle BAC=\angle BPD. Prove that ∠BAC=2∠DPC\angle BAC=2\angle DPC.
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