--description--

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 $n$.

$S(100) = 4\,950$ and $S(1\,200) = 1\,653\,605$.

Find $S({10}^7)$.

--hints--

circumscribedCircles() should return 727227472448913.

assert.strictEqual(circumscribedCircles(), 727227472448913);

--seed--

--seed-contents--

function circumscribedCircles() {

  return true;
}

circumscribedCircles();

--solutions--

// solution required