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<BAC = 2< DPC wanted, BD = 2DC and <BAC = <BPD given

Source: 2015 Indonesia MO Province P2 q3 OSP

December 10, 2020
geometryequal anglesequal segmentsEquilateral

Problem Statement

Given the isosceles triangle ABCABC, where AB=ACAB = AC. Let DD be a point in the segment BCBC so that BD=2DCBD = 2DC. Suppose also that point PP lies on the segment ADAD such that: ∠BAC=∠BPD\angle BAC = \angle BP D. Prove that ∠BAC=2∠DPC\angle BAC = 2\angle DP C.
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