In an acute angled triangle ABC, a certain portion from BC is considered as diameter and a circle is drawn with radius 9. It touches the sides AB and AC. Similarly, taking a certain portion of the side AB and AC as diameter, the radius of these two circles is 3 and 6. The radius of the in-circle of triangle ABC can be expressed in the form a/b, where A and B are co-prime. What is the value of a+b?

I would appreciate some hints rather than a fully-worked out solution. However, if anyone posts a solution, thanks for that too.

## Geometry

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