## Circumscribed Circles

### Problem 373

Published on Saturday, 25th February 2012, 04:00 pm; Solved by 235; Difficulty rating: 75%Every triangle has a circumscribed circle that goes through the three vertices. Consider all integer sided triangles for which the radius of the circumscribed circle is integral as well.

Let S(`n`) be the sum of the radii of the circumscribed circles of all such triangles for which the radius does not exceed `n`.

S(100)=4950 and S(1200)=1653605.

Find S(10^{7}).