i.) Four balls of radius 1 are mutually tangent, three resting on the floor and the fourth resting on the others. A tedrahedron, each of whose edges has length s, is circumscribed around the balls. Find the value of s.
ii.) Suppose that ABCD and EFGH are opposite faces of a retangular solid, with \angle DHC \equal{} 45^{\circ} and \angle FHB \equal{} 60^{\circ}. Find the cosine of ∠BHD. geometry3D geometrytetrahedrontrigonometryinradiusincentersphere