# Three circles in isosceles triangle

I need a little help with this geometry problem, that I need to solve synthetic (I know the analytic solution).

We write in an isosceles triangle those sides are 13 cm, 13 cm, 10 cm three circles. Every circle is tangent to two sides of the triangle and the other two circles. The radii of the circles that are tangent to the base are congruent. Find the radii of the three circles.

I also managed to prove synthetically that the two congruent radii are 2 cm.

• Hint: $(5,12,13)$ is a Pythagorean triple. If you depict the configuration on graph paper, you can get a good idea about the locations of the incenters involved. – Jack D'Aurizio Mar 22 '18 at 19:49