---
id: 5900f4a31000cf542c50ffb6
challengeType: 5
title: 'Problem 311: Biclinic Integral Quadrilaterals'
---
## Description
ABCD is a convex, integer sided quadrilateral with 1 ≤ AB < BC < CD < AD.
BD has integer length. O is the midpoint of BD. AO has integer length.
We'll call ABCD a biclinic integral quadrilateral if AO = CO ≤ BO = DO.
For example, the following quadrilateral is a biclinic integral quadrilateral:
AB = 19, BC = 29, CD = 37, AD = 43, BD = 48 and AO = CO = 23.
Let B(N) be the number of distinct biclinic integral quadrilaterals ABCD that satisfy AB2+BC2+CD2+AD2 ≤ N.
We can verify that B(10 000) = 49 and B(1 000 000) = 38239.
Find B(10 000 000 000).
## Instructions
## Tests
```yml
tests:
- text: euler311() should return 2466018557.
testString: assert.strictEqual(euler311(), 2466018557, 'euler311() should return 2466018557.');
```
## Challenge Seed
```js
function euler311() {
// Good luck!
return true;
}
euler311();
```