Question 13
Let $\Gamma_{1}$ and $\Gamma_{2}$ be circles internally tangent at point $A$, with $\Gamma_{1}$ inside $\Gamma_{2}$. Let $BC$ be a chord of $\Gamma_{2}$ which is tangent to $\Gamma_{1}$ at point $D$. Prove that line $AD$ is the angle bisector of $\angle BAC$.