Question 98
Let $ABC$ be a triangle with centroid $T$ and circumcenter $O$ such that $OT \perp AT$. Let $A'$ be the other intersection of the line $AT$ and the circumcircle of the triangle $ABC$. Let $D$ be the intersection of the lines $BA'$ and $AC$, and let $E$ be the intersection of the lines $CA'$ and $AB$. Prove that the circumcenter of the triangle $ADE$ lies on the circumcircle of the triangle $ABC$.