Difference between revisions of "1982 USAMO Problems/Problem 5"
(Created page with "== Problem == <math>A,B</math>, and <math>C</math> are three interior points of a sphere <math>S</math> such that <math>AB</math> and <math>AC</math> are perpendicular to the dia...") |
|||
| Line 7: | Line 7: | ||
== See Also == | == See Also == | ||
{{USAMO box|year=1982|num-b=4|after=Last Question}} | {{USAMO box|year=1982|num-b=4|after=Last Question}} | ||
| + | {{MAA Notice}} | ||
[[Category:Olympiad Geometry Problems]] | [[Category:Olympiad Geometry Problems]] | ||
Revision as of 18:14, 3 July 2013
Problem
, and 
are three interior points of a sphere 
such that 
and 
are perpendicular to the diameter of through 
, and so that two spheres can be constructed through , 
, and which are both tangent to . Prove that the sum of their radii is equal to the radius of .
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 1982 USAMO (Problems • Resources) | ||
| Preceded by Problem 4 |
Followed by Last Question | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
