15th British Mathematical Olympiad 1979 Problems

15th British Mathematical Olympiad 1979 Problems1.  Find all triangles ABC such that AB + AC = 2 and AD + BD = √5, where AD is the altitude. 2.  Three rays in space have endpoints at O. The angles between the pairs are α, β, γ, where 0 < α < β < γ. Show that there are unique points A, B, C, one on each ray, so that the triangles OAB, OBC, OCA all have perimeter 2s.