Find a radius of circle R.?

Question

Two coplanar circles, one with center at O and the other with center at P are tnagent externally. line AB is a common external tangent segment of the two circles. A third circle with center at R is tangent to Circle O, to Circle P, and to line AB. If a radius of Circle O is 9, and a radius of circle P is 4, find a radius of Circle R. Express your answer as an improper fraction reduced to lowest terms.

Answer 1

where is the figure?

Answer 2

This is a cute problem, and the answer is Sqrt(OP) / Sqrt(O) + Sqrt(P), where O and P are the radii. That is, if O = 9, and P = 4, we have:

R = Sqrt(9*4) / Sqrt(9) + Sqrt(4), or

R = 6/5