Check if three circles fit inside a triangle?

Question

I have thought some time about writing a program that tells me if three circles with given diameters can fit inside a triangle with given side lengths without overlapping (touching is ok) each other. How would one think about doing that?

Answer 1

I would let the incenter circle be one, and the two others be circles on the center lines to two of the angles of the triangle. Actually you can have 3 small circles all touching the incenter circle.