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equal segments starting with segment bisectors in a convex ABCD

Source: Sharygin 2010 Final 8.3

October 2, 2018
geometryequal segmentsbisectionangle bisector

Problem Statement

Let ABCDABCD be a convex quadrilateral and KK be the common point of rays ABAB and DCDC. There exists a point PP on the bisectrix of angle AKDAKD such that lines BPBP and CPCP bisect segments ACAC and BDBD respectively. Prove that AB=CDAB = CD.
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