2000 AIME II Problem 12

The points A, B and C lie on the surface of a sphere with center O and radius 20. It is given that AB=13, BC=14, CA=15, and that the distance from O to triangle ABC is \frac{m\sqrt{n}}k, where m, n, and k are positive integers, m and k are relatively prime, and n is not divisible by the square of any prime. Find m+n+k.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.