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angle bisector wanted, statring with isosceles

Source: VI Soros Olympiad 1990-00 R2 9.3 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 28, 2024
geometryangle bisector

Problem Statement

On the sides BCBC and ACAC of the isosceles triangle ABCABC (AB=BCAB = BC), points EE and DD are marked, respectively, so that DE∥ABDE \parallel AB. On the extendsion of side CBCB beyond the point BB, point KK was arbitrarily marked. Let PP be the intersection point of the lines ABAB and KDKD. Let QQ be the intersection point of the lines AKAK and DEDE. Prove that CACA is the bisector of angle ∠PCQ\angle PCQ.
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