Question 114
Let $C_{1}$ and $C_{2}$ be externally tangent circles with radius $2$ and $3$, respectively. Let $C_{3}$ be a circle internally tangent to both $C_{1}$ and $C_{2}$ at points $A$ and $B$, respectively. The tangents to $C_{3}$ at $A$ and $B$ meet at $T$, and $TA = 4$. Determine the radius of $C_{3}$.