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---
id: 5900f4a31000cf542c50ffb6
title: 'Problem 311: Biclinic Integral Quadrilaterals'
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challengeType: 5
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forumTopicId: 301967
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dashedName: problem-311-biclinic-integral-quadrilaterals
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---
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# --description--
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ABCD is a convex, integer sided quadrilateral with 1 ≤ AB < BC < CD < AD.
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BD has integer length. O is the midpoint of BD. AO has integer length.
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We'll call ABCD a biclinic integral quadrilateral if AO = CO ≤ BO = DO.
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For example, the following quadrilateral is a biclinic integral quadrilateral: AB = 19, BC = 29, CD = 37, AD = 43, BD = 48 and AO = CO = 23.
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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.
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Find B(10 000 000 000).
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# --hints--
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`euler311()` should return 2466018557.
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```js
assert.strictEqual(euler311(), 2466018557);
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```
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# --seed--
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## --seed-contents--
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```js
function euler311() {
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return true;
}
euler311();
```
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# --solutions--
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```js
// solution required
```
