1. ## spherical triangles problem

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.
2. Show that necessarily π < α+β+γ < π +2min{α,β,γ}. Hint: First show that 0< α+β+γ-π <2α

2. Originally Posted by parish_josh
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.
1. Show that necessarily π < α+β+γ < π +2min{α,β,γ}. Hint: First show that 0< α+β+γ-π <2α

What have you tried? How far did you get? Where are you stuck?

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