I'm having trouble understanding this question, it may be out of my current knowledge base, but I won't know until I try.
I desire most a diagram to help me visualize the question. If you have a complete solution then leave it as a spoiler.

Question
Three spheres are tangent to a plane at the vertices of a triangle and tangent to each other. Find the radii of these spheres if the sides of the triangle are 6, 8, 10.

Thanks in advance to the forum

Hi

Here is a view of 2 of the 3 spheres and the plan



One relation between the radii of the 2 spheres is
(x-y)²+a²=(x+y)² or 4xy=a²

Does this help ?