Four balls of radius 1 are mutually tangent
Source: IMO LongList 1988, India 2, Problem 37 of ILL
November 3, 2005
geometry3D geometrytetrahedrontrigonometryinradiusincentersphere
Problem Statement
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 is circumscribed around the balls. Find the value of
ii.) Suppose that and are opposite faces of a retangular solid, with \angle DHC \equal{} 45^{\circ} and \angle FHB \equal{} 60^{\circ}. Find the cosine of