Question 24
Two circles $C_{1}$ and $C_{2}$ of centers $A$ and $B$ are tangent externally at $T$. Let $B D$ be a segment tangent to $C_{1}$ in $D$ and let $T C$ be the segment tangent to both in $T$ with $C \in B D$. If $A T$ is 80 long and $B T$ is 90 long, what is the length of $C D$?