Difference between revisions of "1962 IMO Problems/Problem 7"

(New page: ==Problem== The tetrahedron <math>SABC</math> has the following property: there exist five spheres, each tangent to the edges <math>SA, SB, SC, BC, CA, AB</math>, or to their extensions. ...)
 
m (See Also)
 
Line 12: Line 12:
  
 
{{IMO box|year=1962|num-b=6|after=Last Question}}
 
{{IMO box|year=1962|num-b=6|after=Last Question}}
 +
[[Category:Olympiad Geometry Problems]]
 +
[[Category:3D Geometry Problems]]

Latest revision as of 22:30, 18 July 2016

Problem

The tetrahedron $SABC$ has the following property: there exist five spheres, each tangent to the edges $SA, SB, SC, BC, CA, AB$, or to their extensions.

(a) Prove that the tetrahedron $SABC$ is regular.

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

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

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
Invalid username
Login to AoPS