I read this problem years ago and always wondered how to solve it. I might get some of the details wrong (or use the wrong termonology, its been awhile, apologies in advance) but I'll do my best.

Four circles inside of a triangle with three of the circles each touching one side of the triangle. Each of the three circles touches the forth, which was not touch the triangle.

I believe a radius was given for the first three circles (3, 4, 5 I believe) and the problem wants you to find either the fourth circles radius (or circumference) or maybe the length of the hypotenuse. This number was said to be able to be represented in the form of q/r with q and r being (relatively?) prime.

If anyone could help me remember the actual problem it would be a life saver. Every few weeks this pops in my head and I try working out what it actually was and how to go about solving it.