Difference between revisions of "2006 AIME A Problems/Problem 12"
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[[Category:Intermediate Geometry Problems]] | [[Category:Intermediate Geometry Problems]] | ||
Revision as of 14:57, 25 September 2007
Problem
Find the sum of the values of 
such that 
where is measured in degrees and 
Solution
Observe that 
by the sum-to-product formulas. Defining 
and 
, we have 
. But 
, so we require 
, 
, 
, or 
.
Hence the solution set is 
and thus 
.
See also
| 2006 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
