Application of the Sine Rule

Let ABC be a triangle. Let and be the radii of two circles through A, touching BC at B and C, respectively. Prove that , where is the radius of the circumcircle of ABC. (Source: Geometry Revisited by Coxeter & Greitzer, 1967, p3)
1. Visualise the problem by moving F & G so that both FB and GC are perpendicular to BC. 2. Observe the numerical results. 3. Repeat 1 & 2 for various triangles, ABC. 4. What construction(s) might be helpful to prove the desired result? 5. Hint: Use the extended Law of Sines, /sin A = /sin B = /sin C = .