Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 8"
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==Problem== | ==Problem== | ||
| − | + | [[Image:2006 CyMO-8.PNG|250px|right]] | |
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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> | |
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| − | B | ||
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| − | C | ||
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| − | D | ||
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==Solution== | ==Solution== | ||
Revision as of 10:41, 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
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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 | ||
