2006 Cyprus MO/Lyceum/Problem 8
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
In the quadrilateral , we have three isosceles triangles , , and . Those are congruent to each other, as well as , , and . Also, is congruent to . Thus we have two figures of equal area: and a combination of two figures: and . Since the area of the whole star is 1, the area of is .
See also
2006 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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