yaworsw/euler-manager

---
:id: 311
:name: Biclinic Integral Quadrilaterals
:url: https://projecteuler.net/problem=311
:content: "ABCD is a convex, integer sided quadrilateral with 1 ≤ AB \\< BC \\< CD
  \\< AD.  \nBD has integer length. O is the midpoint of BD. AO has integer length.
  \ \nWe'll call ABCD a _biclinic integral quadrilateral_ if AO = CO ≤ BO = DO.\n\nFor
  example, the following quadrilateral is a biclinic integral quadrilateral:  \nAB
  = 19, BC = 29, CD = 37, AD = 43, BD = 48 and AO = CO = 23.\n\n ![p311_biclinic.gif]({{
  images_dir }}/p311_biclinic.gif)\n\nLet B(<var>N</var>) be the number of distinct
  biclinic integral quadrilaterals ABCD that satisfy AB<sup>2</sup>+BC<sup>2</sup>+CD<sup>2</sup>+AD<sup>2</sup>
  ≤ <var>N</var>.  \nWe can verify that B(10 000) = 49 and B(1 000 000) = 38239.\n\nFind
  B(10 000 000 000).\n\n"