I don't understand this problem that well. Any hints?

I thought that if the two stars are at opposite ends of the orbit, won't the gravitational forces from one cancel out the forces from the other star?

Then won't the period just be Kepler's Third law?

T^2 = (r^3)*(4pi^2)/(GM), G = universal gravitational constant, M = mass of central star, T = period of revolution, r = radius of the orbit, pi = 3.14159...