Question 33
Let $O$ be the center of the circumcircle of $\triangle ABC$. A line $t$ is tangent to the circumcircle of $\triangle BOC$ and meets the sides $AB$ and $AC$ at $D$ and $E$, respectively ($D, E \not\equiv A$). The point $A'$ is the reflection of $A$ in the line $t$. Prove that the circumcircles of $\triangle A'DE$ and $\triangle ABC$ are tangent. (Dusan Djukic)