## Inscribed circles of triangles with one angle of 60 degrees

### Problem 195

Published on Friday, 23rd May 2008, 02:00 pm; Solved by 839; Difficulty rating: 75%Let's call an integer sided triangle with exactly one angle of 60 degrees a 60-degree triangle.

Let `r` be the radius of the inscribed circle of such a 60-degree triangle.

There are 1234 60-degree triangles for which `r` ≤ 100.

Let T(`n`) be the number of 60-degree triangles for which `r` ≤ `n`, so

T(100) = 1234, T(1000) = 22767, and T(10000) = 359912.

Find T(1053779).