# Problem 496: Incenter and circumcenter of triangle
Given an integer sided triangle ABC: Let I be the incenter of ABC. Let D
be the intersection between the line AI and the circumcircle of ABC (A ≠
D). We define F(L) as the sum of BC for the triangles ABC that satisfy
AC = DI and BC ≤ L. For example, F(15) = 45 because the triangles ABC
with (BC,AC,AB) = (6,4,5), (12,8,10), (12,9,7), (15,9,16) satisfy the
conditions. Find F(109).