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Circumscribed Circles

Published on Saturday, 25th February 2012, 04:00 pm; Solved by 282;
Difficulty rating: 75%

Problem 373

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(107).