Question 7
Two circles are tangent to each other from outside at a point $A$ and to a third circle $\Gamma$ from inside at points $B$ and $C$. Let $D$ be the midpoint of the secant of $\Gamma$ which is tangent to the smaller circles at $A$. Show that $A$ is the incenter of the triangle $BCD$ if the centers of the circles are not collinear.