Question 98
Let $ABC$ be a triangle, and let $I$ be its incenter. Let $D$ be the reflection of $I$ across side $AB$, and let $E$ be the reflection of $I$ across side $AC$.
Prove that the circumcircles of triangles $BID$ and $CIE$ are tangent to each other.
Prove that the circumcircles of triangles $BID$ and $CIE$ are tangent to each other.