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Equal angles imply equal lengths

Source: IMSC 2024 Day 1 Problem 2

June 28, 2024
geometryimsc

Problem Statement

Let ABCABC be an acute angled triangle and let P,QP, Q be points on AB,ACAB, AC respectively, such that PQPQ is parallel to BCBC. Points X,YX, Y are given on line segments BQ,CPBQ, CP respectively, such that ∠AXP=∠XCB\angle AXP = \angle XCB and ∠AYQ=∠YBC\angle AYQ = \angle YBC. Prove that AX=AYAX = AY.
Proposed by Ervin Macicˊ,\acute{c}, Bosnia and Herzegovina
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