MathDB

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Part of 1976 IMO Longlists

Problems(1)

Regular pentagon and spheres at each vertex

Source:

1/11/2011
A regular pentagon A1A2A3A4A5A_1A_2A_3A_4A_5 with side length ss is given. At each point AiA_i, a sphere KiK_i of radius s2\frac{s}{2} is constructed. There are two spheres K1K_1 and K2K_2 each of radius s2\frac{s}{2} touching all the five spheres Ki.K_i. Decide whether K1K_1 and K2K_2 intersect each other, touch each other, or have no common points.
geometry3D geometryspheregeometry unsolved