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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