Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 11"
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<math>[OAB]=8</math> | <math>[OAB]=8</math> | ||
− | <math>[ | + | <math>[OA\Gamma]=\frac{\frac{4}{3}*4}{2}=\frac{8}{3}</math> |
− | <math>[ | + | <math>[OB\Gamma]=[OAB]-[OA\Gamma]=\frac{16}{3}</math> |
− | <math>\frac{[ | + | <math>\frac{[OA\Gamma]}{[OB\Gamma]}=\frac{1}{2} \Rightarrow \mathrm {(D)}</math> |
==See also== | ==See also== | ||
{{CYMO box|year=2006|l=Lyceum|num-b=10|num-a=12}} | {{CYMO box|year=2006|l=Lyceum|num-b=10|num-a=12}} |
Revision as of 22:49, 19 October 2007
Problem
The lines and intersect at the point . If the line intersects the axes and to the points and respectively, then the ratio of the area of the triangle to the area of the triangle equals
A.
B.
C.
D.
E.
Solution
We find some coordinates:
We find the area of triangles:
See also
2006 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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 |