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Circumscribed circles

Source: 2020 Serbian MO, Problem 3

September 26, 2020
circumcircleTrianglegeometryangle

Problem Statement

We are given a triangle ABCABC. Points DD and EE on the line ABAB are such that AD=ACAD=AC and BE=BCBE=BC, with the arrangment of points D−A−B−ED - A - B - E. The circumscribed circles of the triangles DBCDBC and EACEAC meet again at the point X≠CX\neq C, and the circumscribed circles of the triangles DECDEC and ABCABC meet again at the point Y≠CY\neq C. Find the measure of ∠ACB\angle ACB given the condition DY+EY=2XYDY+EY=2XY.
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