--description--

Given is an integer sided triangle $ABC$ with $BC ≤ AC ≤ AB$. $k$ is the angular bisector of angle $ACB$. $m$ is the tangent at $C$ to the circumscribed circle of $ABC$. $n$ is a line parallel to $m$ through $B$.

The intersection of $n$ and $k$ is called $E$.

How many triangles $ABC$ with a perimeter not exceeding $100\,000$ exist such that $BE$ has integral length?

--hints--

angularBisectorAndTangent() should return 1137208419.

assert.strictEqual(angularBisectorAndTangent(), 1137208419);

--seed--

--seed-contents--

function angularBisectorAndTangent() {

  return true;
}

angularBisectorAndTangent();

--solutions--

// solution required