MathNet 2021 — Part 08 Question 73

Let $ABC$ be a triangle with $AB\ne AC$. Let $I$ be its incenter, $\gamma$ its incircle, and $D$ the midpoint of $BC$. The tangent to $\gamma$ through $D$ other than $BC$ touches $\gamma$ at $E$. Prove that $AE$ and $DI$ are parallel.