# Application of the Sine Rule

- Author:
- Maurice OReilly

- Topic:
- Sine

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 = .