Let P be a point in triangle ABC such that angles APB, BPC, and CPA are all 120 degrees. Can lines AB, AC, BC, PA, PB, and PC all have integral lengths?

(In reply to

re: on another look by Nishant)

"D=-3*y^2 + 4*c^2=0"

Why do you assume that for D to be a square that it must be 0? A counterexample is c=37, y=40, D=676=26^2