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Angle bisectors and parallel

Source: CSMO 2019 Grade 11 Problem 6

July 31, 2019
geometry

Problem Statement

In △ABC\triangle ABC, AB>ACAB>AC, the bisectors of ∠ABC,∠ACB\angle ABC, \angle ACB meet sides AC,ABAC,AB at D,ED,E respectively. The tangent at AA to the circumcircle of △ABC\triangle ABC intersects EDED extended at PP. Suppose that AP=BCAP=BC. Prove that BD∥CPBD\parallel CP.
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