We apply the law of cosines to each of three isosceles triangles in Figure 9 having a vertex at the center of the heptagon, two edges of length R and base of length rk, where k = 1,2, 3. The corresponding vertex angles are θk, where θ1 = 2π/7, θ2 = 4π/7, θ3 = 6π/7. The law of cosines for the isosceles triangle with vertex angle θk states that