Difference between revisions of "1990 AIME Problems/Problem 12"
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== Problem == | == Problem == | ||
| + | A regular 12-gon is inscribed in a circle of radius 12. The sum of the lengths of all sides and diagonals of the 12-gon can be written in the form | ||
| + | <center><math>a + b \sqrt{2} + c \sqrt{3} + d \sqrt{6},</math></center> | ||
| + | where <math>a^{}_{}</math>, <math>b^{}_{}</math>, <math>c^{}_{}</math>, and <math>d^{}_{}</math> are positive integers. Find <math>a + b + c + d^{}_{}</math>. | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
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== See also == | == See also == | ||
| − | + | {{AIME box|year=1990|num-b=11|num-a=13}} | |
Revision as of 01:36, 2 March 2007
Problem
A regular 12-gon is inscribed in a circle of radius 12. The sum of the lengths of all sides and diagonals of the 12-gon can be written in the form
where 
, 
, 
, and 
are positive integers. Find 
.
Solution
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See also
| 1990 AIME (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 | ||
