Difference between revisions of "1982 USAMO Problems/Problem 5"
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Revision as of 22:17, 18 July 2016
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
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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.