yaworsw/euler-manager

---
:id: 257
:name: Angular Bisectors
:url: https://projecteuler.net/problem=257
:content: "Given is an integer sided triangle ABC with sides a ≤ b ≤ c. (AB = c, BC
  = a and AC = b).  \nThe angular bisectors of the triangle intersect the sides at
  points E, F and G (see picture below).\n\n ![p257_bisector.gif]({{ images_dir }}/p257_bisector.gif)
  \ \n\nThe segments EF, EG and FG partition the triangle ABC into four smaller triangles:
  AEG, BFE, CGF and EFG.  \nIt can be proven that for each of these four triangles
  the ratio area(ABC)/area(subtriangle) is rational.  \nHowever, there exist triangles
  for which some or all of these ratios are integral.\n\nHow many triangles ABC with
  perimeter≤100,000,000 exist so that the ratio area(ABC)/area(AEG) is integral?\n\n"