We are given a triangle ABC. Points D and E on the line AB are such that AD=AC and BE=BC, with the arrangment of points D−A−B−E. The circumscribed circles of the triangles DBC and EAC meet again at the point X=C, and the circumscribed circles of the triangles DEC and ABC meet again at the point Y=C. Find the measure of ∠ACB given the condition DY+EY=2XY. circumcircleTrianglegeometryangle