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Surprisingly Easy Geo

Source: 2019 China Second Round P1

September 8, 2019
geometryChina second round

Problem Statement

In acute triangle △ABC\triangle ABC, MM is the midpoint of segment BCBC. Point PP lies in the interior of △ABC\triangle ABC such that APAP bisects ∠BAC\angle BAC. Line MPMP intersects the circumcircles of △ABP,△ACP\triangle ABP,\triangle ACP at D,ED,E respectively. Prove that if DE=MPDE=MP, then BC=2BPBC=2BP.
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