Problem 311

Biclinic Integral Quadrilaterals

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 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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These problems are part of
Project Euler
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