Question 152
Let $ABC$ be a triangle with incenter $I$ and ex-center $J$. Denote $K$ as the reflection of $A$ over $BC$ and take $X$, $Y$ on the opposite rays of $BA$, $CA$ such that $XB = BC = CY$. Let $T$ be the circumcenter of $AXY$. Prove that:
a) $OJ \perp XY$ and $AT$ is tangent to $(AIK)$.
b) $R_{(T)} = OJ$ and $TJ \perp BC$.
a) $OJ \perp XY$ and $AT$ is tangent to $(AIK)$.
b) $R_{(T)} = OJ$ and $TJ \perp BC$.