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 \(m/n,\) where \(m\) and \(n\) are relatively prime positive integers. Find \(m + n.\)

(第十九届AIME1 2001 第12题)