Question 76
Quadrilateral $A B C D$ is inscribed in circle $\Gamma$. Segments $A C$ and $B D$ intersect at $E$. Circle $\gamma$ passes through $E$ and is tangent to $\Gamma$ at $A$. Suppose that the circumcircle of triangle $B C E$ is tangent to $\gamma$ at $E$ and is tangent to line $C D$ at $C$. Suppose that $\Gamma$ has radius $3$ and $\gamma$ has radius $2$. Compute $B D$.