1962 IMO Problems/Problem 7

Problem

The tetrahedron has the following property: there exist five spheres, each tangent to the edges , or to their extensions.

(a) Prove that the tetrahedron is regular.

(b) Prove conversely that for every regular tetrahedron five such spheres exist.

Solution

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See Also

1962 IMO (Problems) • Resources
Preceded by Problem 6	1 • 2 • 3 • 4 • 5 • 6	Followed by Last Question
All IMO Problems and Solutions