Three spheres are tangent to a plane at the vertices of a triangle and are tangent to each other. Find the radii of these spheres if the sides of the triangle are 6, 8, and 10.
My go at it: We can turn this into a 2d geo problem. We let the radii's be x,y, and z. Then x+z = 6, z+y = 8 and x+y = 10. Solving the system of equations, we get that x,y,z = 4,6,2.
However my answers did not match the answer key and I do not where I went wrong. Can anybody help? thanks.