Question 4
Let $ABC$ be a triangle. Points $D,E$ lie on line $AB$, in the order $D-A-B-E$, with $AD=AC$ and $BE=BC$. The circumcircles of $DBC,EAC$ meet at $X\neq C$, and the circumcircles of $DEC,ABC$ meet at $Y\neq C$. If $DY+EY=2XY$, determine $\angle ACB$.