Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 8"
I like pie (talk | contribs) (Standardized answer choices) |
|||
| Line 1: | Line 1: | ||
==Problem== | ==Problem== | ||
| − | + | [[Image:2006 CyMO-8.PNG|250px|right]] | |
| − | [[Image:2006 CyMO-8.PNG|250px]] | ||
| − | |||
In the figure <math>AB\Gamma \Delta E</math> is a regular 5-sided polygon and <math>Z</math>, <math>H</math>, <math>\Theta</math>, <math>I</math>, <math>K</math> are the points of intersections of the extensions of the sides. | In the figure <math>AB\Gamma \Delta E</math> is a regular 5-sided polygon and <math>Z</math>, <math>H</math>, <math>\Theta</math>, <math>I</math>, <math>K</math> are the points of intersections of the extensions of the sides. | ||
If the area of the "star" <math>AHB\Theta \Gamma I\Delta KEZA</math> is 1, then the area of the shaded quadrilateral <math>A\Gamma IZ</math> is | If the area of the "star" <math>AHB\Theta \Gamma I\Delta KEZA</math> is 1, then the area of the shaded quadrilateral <math>A\Gamma IZ</math> is | ||
| − | + | <math>\mathrm{(A)}\ \frac{2}{3}\qquad\mathrm{(B)}\ \frac{1}{2}\qquad\mathrm{(C)}\ \frac{3}{7}\qquad\mathrm{(D)}\ \frac{3}{10}\qquad\mathrm{(E)}\ \text{None of these}</math> | |
| − | |||
| − | B | ||
| − | |||
| − | C | ||
| − | |||
| − | D | ||
| − | |||
| − | |||
==Solution== | ==Solution== | ||
Revision as of 09:41, 27 April 2008
Problem
In the figure 
is a regular 5-sided polygon and 
, 
, 
, 
, 
are the points of intersections of the extensions of the sides.
If the area of the "star" 
is 1, then the area of the shaded quadrilateral 
is
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 2006 Cyprus MO, Lyceum (Problems) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
