Harmonious!

Level pending

Two circles \(C_{1}\) & \(C_{2}\)with radii 4 and 9 units respectively touch each other externally at point P. Let AB be the common tangent to the circles and it does not pass through the point P.Now,another circle is drawn so that it touches the previous two circles (externally) as well as the common tangent AB.

The radius of this new circle can be expressed as the ratio of two co-prime integers as \(\frac{m}{n}\).What is the value of m+n ?

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