Geometry question involving circles and similar triangles

Question

If I have three circles inside an isoceles triangle, all tangent to the triangle and with centers on the vertex angle's bisection, what will be the radius of the one in the middle, as a function of the radii of the other two circles, to which the middle one is tangent?



Answer 1

I do NOT believe this is possible.

The bottom circle is constrained to be tangent to 4 points: the base, the 2 sides and the middle circle...that is not possible because 3 points determine a circle.

I think this problem has either been incorrectly stated or incorrectly conceived.

Or maybe I do not understand the problem...maybe the bottom circle need not be tangent to all 3 sides of the triangle, but you have not made that clear!