Question 12
A sphere is inscribed in the tetrahedron whose vertices are $A = (6, 0, 0),$ $B = (0, 4, 0),$ $C = (0, 0, 2),$ and $D = (0, 0, 0).$ The radius of the sphere is $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$