Question 87
Let the $O$ be the center of the sharp triangle $ABC$ outlined circles $\mathcal{K}$. The bisector of the internal angle at $A$ intersects the $\mathcal{K}$ circle at the $D$ point, and the inner angle bisector at the $B$ intersects the circle $\mathcal{K}$ still at the $E$ point. Let's mark with the $I$ center of the $ABC$ triangle of the inscribed circle. What is the size of the $\angle ACB$ angle if the points $D, E, O$ and $I$ lie on the same circle?