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.

Three spheres are tangent to a plane at the vertices of a triangle and are tangent to each other. Denote the points where spheres are tangent to the lane A, B, C. You get a triangle ABC with lengths of sides 6, 8 and 10. Denote the projections of the tangent points between spheres on the pane.
Then 
 
and 
.

Add all these three equations: and substract each equation from  :

.
Then
are spheres' radii.