Question 69
Let $I$ and $O$ be the incenter and the circumcenter, respectively, of the $\triangle ABC$.
Draw a straight line $L$ that is parallel to $BC$ and tangent to the incircle of $\triangle ABC$.
Suppose that $L$ and $IO$ intersect at the point $X$, and $Y$ is a point on $L$ such that $YI$ is perpendicular to $IO$.
Prove that $A, X, O, Y$ are concyclic.
Supplemental figure:
Draw a straight line $L$ that is parallel to $BC$ and tangent to the incircle of $\triangle ABC$.
Suppose that $L$ and $IO$ intersect at the point $X$, and $Y$ is a point on $L$ such that $YI$ is perpendicular to $IO$.
Prove that $A, X, O, Y$ are concyclic.
Supplemental figure: