Problem

Source: Sharygin 2006 XI CR 26

Tags: geometry, cone, 3D geometry, Concyclic, tangent circles



Four cones are given with a common vertex and the same generatrix, but with, generally speaking, different radii of the bases. Each of them is tangent to two others. Prove that the four tangent points of the circles of the bases of the cones lie on the same circle.