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

## Description
<section id='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).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler410()</code> should return 799999783589946600.
    testString: assert.strictEqual(euler410(), 799999783589946600);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler410() {
  // Good luck!
  return true;
}

euler410();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>