A problem by Ankush Tiwari

Level pending

Two circles of radii 9 and 16 units touch each other externally. Let r r be the radius of a circle which touches these two circles as well as the common tangent to the two circles. The value of r r can be expressed as a b \frac{a}{b} where a a and b b are positive coprime integers. Find a + b a + b .


The answer is 193.

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