Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 8"
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==Problem== | ==Problem== | ||
| − | {{ | + | <div style="float:right"> |
| + | [[Image:2006 CyMO-8.PNG|250px]] | ||
| + | </div> | ||
| + | |||
| + | 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 | ||
| + | |||
| + | A. <math>\frac{2}{3}</math> | ||
| + | |||
| + | B. <math>\frac{1}{2}</math> | ||
| + | |||
| + | C. <math>\frac{3}{7}</math> | ||
| + | |||
| + | D. <math>\frac{3}{10}</math> | ||
| + | |||
| + | E. None of these | ||
==Solution== | ==Solution== | ||
Revision as of 22:23, 17 October 2007
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
A. 
B. 
C. 
D. 
E. None of these
Solution
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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 | ||
