Star inside circle

We can make bigger regular pentagon by connecting the vertices of the triangles on the circle. Let the side of this bigger pentagon is x, and a is the longer sides of the isosceles triangle. We make connection between a and R the radius of the circle by using cos rule. x^2 = 2R^2 ( 1 – cos 72), x^2 = 2a^2 ( 1 – cos 108), then, a^2 = R^2 ( 1 – cos 72)/(1 – cos 108). The different between areas of blue region and yellow region = π R^2 – 10 (a^2 / 2) sin 36= 43. Then we found R = 5.2