Question 97
Let $ABC$ be a triangle with $AB = AC \neq BC$ and let $I$ be the centre of its incircle. The line $BI$ meets $AC$ at $D$, and the perpendicular to $AC$ through $D$ meets $AI$ at $E$. Show that the reflection of $I$ in the line $AC$ lies on the circumcircle of the triangle $BDE$.