yaworsw/euler-manager

---
:id: 264
:name: Triangle Centres
:url: https://projecteuler.net/problem=264
:content: "Consider all the triangles having:\n\n- All their vertices on <dfn title=\"Integer
  coordinates\">lattice points</dfn>.\n- <dfn title=\"Centre of the circumscribed
  circle\">Circumcentre</dfn> at the origin O.\n- <dfn title=\"Point where the three
  altitudes meet\">Orthocentre</dfn> at the point H(5, 0).\n\nThere are nine such
  triangles having a perimeter ≤ 50.  \nListed and shown in ascending order of their
  perimeter, they are:\n\n| A(-4, 3), B(5, 0), C(4, -3)  \nA(4, 3), B(5, 0), C(-4,
  -3)  \nA(-3, 4), B(5, 0), C(3, -4)  \n  \n  \nA(3, 4), B(5, 0), C(-3, -4)  \nA(0,
  5), B(5, 0), C(0, -5)  \nA(1, 8), B(8, -1), C(-4, -7)  \n  \n  \nA(8, 1), B(1, -8),
  C(-4, 7)  \nA(2, 9), B(9, -2), C(-6, -7)  \nA(9, 2), B(2, -9), C(-6, 7)  \n | ![p264_TriangleCentres.gif]({{
  images_dir }}/p264_TriangleCentres.gif) |\n\nThe sum of their perimeters, rounded
  to four decimal places, is 291.0089.\n\nFind all such triangles with a perimeter
  ≤ 10<sup>5</sup>.  \nEnter as your answer the sum of their perimeters rounded to
  four decimal places.\n\n"