(;) Semicolon Math: Insphere Exsphere

Define an insphere of a tetrahedron to be the sphere that is internally tangent to all four faces of the tetrahedron, lying entirely in the interior and boundary of the tetrahedron. Define an exsphere of a tetrahedron to be a sphere that is externally tangent to one face of the tetrahedron and also tangent to the planes containing the other three faces. Suppose a tetrahedron has the four vertices \(A=(0,0,0), B =(6,0,0), C=(0,6,0), D=(0,0,6)\). Let \(r\) denote the radius of its insphere. Let \(R_a\) be the radius of the exsphere that is tangent externally to face \(BCD\) and also tangent to the planes containing \(ABC, ABD,\) and \(ACD\). Find \(R_a^2 + r^2 + R_a + r\).