A circle of radius 1 has four circles \omega_1, \omega_2, \omega_3, and \omega_4 of equal radius internally tangent to it, so that \omega_1 is tangent to \omega_2, which is tangent to \omega_3, which is tangent to \omega_4, which is tangent to \omega_1, as shown. The radius of the circle externally tangent to \omega_1, \omega_2, \omega_3, and \omega_4 has radius r. If r = a - \sqrt{b} for positive integers a and b, compute a + b.