Question 69
Let $O$ be the circumcentre of the acute triangle $ABC$ and denote the circumcircle by $\kappa$. The bisector of the inner angle at $A$ meets $\kappa$ again at $D$. The bisector of the inner angle at $B$ meets $\kappa$ again at $E$. Let $I$ denote the incentre of the triangle $ABC$. How much does the angle $\angle ACB$ measure if the points $D, E, O$ and $I$ lie on the same circle?