Question 135
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 $IC = ID$.