Question 146
Let $\mathcal{K}$ be the circumcircle and $\mathcal{I}$ the incenter of the triangle $ABC$. Denote by $D$ the midpoint of the arc $BC$ of the circle $\mathcal{K}$ which does not contain the point $A$, and by $E$ the midpoint of the arc $CA$ of the circle $\mathcal{K}$ which does not contain the point $B$. Let $F$ be the mirror image of the point $\mathcal{I}$ by reflection across the side $AB$ and suppose that $F$ lies on the circle $\mathcal{K}$. What is the size of the angle $\angle DFE$?