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]] | ||
Revision as of 22:30, 18 July 2016
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
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 | ||
