---
id: 5900f5071000cf542c510018
title: 'Problem 410: Circle and tangent line'
challengeType: 5
forumTopicId: 302079
dashedName: problem-410-circle-and-tangent-line
---

# --description--

Let C be the circle with radius r, x2 + y2 = r2. We choose two points P(a, b) and Q(-a, c) so that the line passing through P and Q is tangent to C.

For example, the quadruplet (r, a, b, c) = (2, 6, 2, -7) satisfies this property.

Let F(R, X) be the number of the integer quadruplets (r, a, b, c) with this property, and with 0 < r ≤ R and 0 < a ≤ X.

We can verify that F(1, 5) = 10, F(2, 10) = 52 and F(10, 100) = 3384. Find F(108, 109) + F(109, 108).

# --hints--

`euler410()` should return 799999783589946600.

```js
assert.strictEqual(euler410(), 799999783589946600);
```

# --seed--

## --seed-contents--

```js
function euler410() {

  return true;
}

euler410();
```

# --solutions--

```js
// solution required
```