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Line parallel to angle bisector

Source: Sharygin Geometry Olympiad Correspondence round 2016 P-4 Grade 8

February 20, 2017
geometryangle bisector

Problem Statement

In quadrilateral ABCDABCD, ∠B=∠D=90\angle B = \angle D = 90 and AC=BC+DCAC = BC + DC. Point PP of ray BDBD is such that BP=ADBP = AD. Prove that line CPCP is parallel to the bisector of angle ABDABD.
(Proposed by A.Trigub)
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