Problems(1)
Let ABC be an acute angled triangle and let P,Q be points on AB,AC respectively, such that PQ is parallel to BC. Points X,Y are given on line segments BQ,CP respectively, such that ∠AXP=∠XCB and ∠AYQ=∠YBC. Prove that AX=AY. Proposed by Ervin Macicˊ, Bosnia and Herzegovina geometryimsc