Difference between revisions of "2013 AMC 12B Problems/Problem 16"
(→Problem) |
|||
| Line 1: | Line 1: | ||
==Problem== | ==Problem== | ||
| − | + | Let <math>ABCDE</math> be an equiangular convex pentagon of perimeter <math>1</math>. The pairwise intersections of the lines that extend the sides of the pentagon determine a five-pointed star polygon. Let <math>s</math> be the perimeter of this star. What is the difference between the maximum and the minimum possible values of <math>s</math>. | |
| − | <math>\textbf{(A)}\ | + | <math>\textbf{(A)}\ 0 \qquad \textbf{(B)}\ \frac{1}{2} \qquad \textbf{(C)}\ \frac{\sqrt{5}-1}{2} \qquad \textbf{(D)}\ \frac{\sqrt{5}+1}{2} \qquad \textbf{(E)}\ \sqrt{5}</math> |
| + | |||
| + | ==Solution== | ||
| + | |||
| + | == See also == | ||
| + | {{AMC12 box|year=2013|ab=B|num-b=15|num-a=17}} | ||
==Solution== | ==Solution== | ||
Revision as of 17:10, 22 February 2013
Contents
Problem
Let 
be an equiangular convex pentagon of perimeter 
. The pairwise intersections of the lines that extend the sides of the pentagon determine a five-pointed star polygon. Let 
be the perimeter of this star. What is the difference between the maximum and the minimum possible values of .
Solution
See also
| 2013 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 15 |
Followed by Problem 17 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
Solution
See also
| 2013 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 15 |
Followed by Problem 17 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
