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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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< img class = "img-responsive center-block" alt = "quadrilateral ABCD, with point O, an midpoint of BD" src = "https://cdn.freecodecamp.org/curriculum/project-euler/biclinic-integral-quadrilaterals.gif" style = "background-color: white; padding: 10px;" >
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Let $B(N)$ be the number of distinct biclinic integral quadrilaterals $ABCD$ that satisfy ${AB}^2 + {BC}^2 + {CD}^2 + {AD}^2 ≤ N$. We can verify that $B(10\\,000) = 49$ and $B(1\\,000\\,000) = 38239$.
Find $B(10\\,000\\,000\\,000)$.
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# --hints--
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`biclinicIntegralQuadrilaterals()` should return `2466018557` .
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```js
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assert.strictEqual(biclinicIntegralQuadrilaterals(), 2466018557);
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```
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# --seed--
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## --seed-contents--
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```js
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function biclinicIntegralQuadrilaterals() {
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return true;
}
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biclinicIntegralQuadrilaterals();
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```
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# --solutions--
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```js
// solution required
```