#### parish_josh

##### New member

- Joined
- Nov 27, 2013

- Messages
- 1

- Let T be a spherical triangle with angles α ,β, γ. Let A, B, and C be the great circles of S^2 that contain each of the three edges of T . Show that these great circles subdivide the sphere S^2 into eight spherical triangles whose angles are all of the form α ,β, γ or π –α, π - β, π –γ.
- Show that necessarily π < α+β+γ < π +2min{α,β,γ}. Hint: First show that 0< α+β+γ-π <2α