Question 5
Equilateral triangle $T$ is inscribed in circle $A,$ which has radius $10.$ Circle $B$ with radius $3$ is internally tangent to circle $A$ at one vertex of $T.$ Circles $C$ and $D,$ both with radius $2,$ are internally tangent to circle $A$ at the other two vertices of $T.$ Circles $B,$ $C,$ and $D$ are all externally tangent to circle $E,$ which has radius $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$
