Question 75
The point $D$ lies on the side $AB$ of $\triangle ABC$ with circumcircle $k$. Denote by $I$ and $J$ the centers of the circles touching $k$, and the segments $AB$ and $CD$. Assume that the points $A, B, I$ and $J$ are concyclic. Prove that $D$ is the tangent point of $AB$ and the excircle to this side.