IMO 1988 LL INA42

(a) Four balls of radius 1 are mutually tangent, three resting an the floor

imolonglistmathematicsolympiad

IMO 1988 LL INA42

Origin: INA

Problem

(a) Four balls of radius 1 are mutually tangent, three resting an the floor and the fourth resting on the others. A tetrahedron, each of whose edges has length s, is circumscribed around the balls. Find the value of s. (b) Suppose that ABCD and EFGH are opposite faces of a rectangu- lar solid, with \angleDHC = 45◦and \angleFHB = 60◦. Find the cosine of \angleBHD.