A Parallelogram and 2 Circles

Geometry Level 4

In Parallelogram ABCD, AB=13AB=13, BC=11BC=11, and AC=20AC=20. Two congruent circles are inscribed in ACD\triangle ACD and ACB\triangle ACB as shown in the figure.

The shortest distance between the centers of the two inscribed circles can be expressed in the form aba\sqrt{b}. Where bb is a square-free integer. Find the value of a+ba+b.

  • Found this somewhere.
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