# Problem 410: Circle and tangent line
Let C be the circle with radius r, x2 + y2 = r2. We choose two points
P(a, b) and Q(-a, c) so that the line passing through P and Q is tangent
to C. For example, the quadruplet (r, a, b, c) = (2, 6, 2, -7) satisfies
this property. Let F(R, X) be the number of the integer quadruplets (r,
a, b, c) with this property, and with 0 < r ≤ R and 0 < a ≤ X. We
can verify that F(1, 5) = 10, F(2, 10) = 52 and F(10, 100) = 3384. Find
F(108, 109) + F(109, 108).