Difference between revisions of "1990 AIME Problems/Problem 12"
m |
|||
Line 1: | Line 1: | ||
− | |||
== 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}} | ||
+ | |||
== 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
![$a + b \sqrt{2} + c \sqrt{3} + d \sqrt{6},$](http://latex.artofproblemsolving.com/5/5/0/55005a9cbb9e5beb3816e1b71f0db8efd1407133.png)
where ,
,
, and
are positive integers. Find
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
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 |