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Bundeswettbewerb Mathematik 1994 Problem 2.3

Source: Bundeswettbwerb Mathematik 1994 Round 2

October 21, 2022
geometry3D geometrysphereconetouching

Problem Statement

Let AA and BB be two spheres of different radii, both inscribed in a cone KK. There are mm other, congruent spheres arranged in a ring such that each of them touches A,B,KA, B, K and two of the other spheres. Prove that this is possible for at most three values of m.m.
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