Circles of radii $36$ and $9$ touch externally. The radius of the circle which touches the two circles externally and also their common tangent is :

Using the formula for the radius of a circle touching two externally tangent circles and their direct common tangent, r equals r1 times r2 divided by the square of the quantity of the square root of r1 plus the square root of r2. Substituting the given radii r1 equals 36 and r2 equals 9, we get r equals 324 divided by the square of the quantity of 6 plus 3. This simplifies to 324 divided by 81, which results in a radius of 2.

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