Consider an equilateral triangle T. Suppose that f is analytic inside of T and satisfies that |f(z)| ≤ 8 on one side of the triangle, while |f(z)| ≤ 1 on the other two sides. Prove that |f(c)| ≤ 2, where c is the center of T.
I know that all of the angles are π/3, or 60 degrees. I know that I have to find the relation between 2 and 8, but I don't know how or where to start. Apparently this can be done in one line, but I am completely stumped.