MathDB

Torus

\mathcal T

is the surface produced by revolving a circle with radius

3

around an axis in the plane a distance

6

from the center of the circle. When a sphere of radius

11

rests inside

\mathcal T

, it is internally tangent to

\mathcal T

along a circle with radius

r_{i}

, and when it rests outside

\mathcal T

, it is externally tangent along a circle with radius

r_{o}

. The difference

r_{i}-r_{o}=\tfrac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m+n

Problem Statement