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 21:49, 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 |