Iranian Mathematical Olympiad

Given two intersecting circles ${\omega }_1,{\omega }_2$. Points $A,C$ lie on ${\omega }_1$ and points $B,D$ lie on ${\omega }_2$ so that $AB,CD$ are common tangents of ${\omega }_1,{\omega }_2$. Let $M$ be the midpoint of $AB$. Tangent lines through $M$ to ${\omega }_1,{\omega }_2$ (other than $AB$) intersect $CD$ at $Y,X$. If $I$ be the incenter of triangle $MXY$, prove that $IC=ID$.