Difference between revisions of "2007 AIME I Problems/Problem 12"
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| − | The [[union]] of the area is equal to <math>2</math> times the area of <math>\triangle ABC</math>, minus the | + | The [[union]] of the area is equal to <math>2</math> times the area of <math>\triangle ABC</math>, minus the intersection of the area of the two triangles. |
== See also == | == See also == | ||
{{AIME box|year=2007|n=I|num-b=11|num-a=13}} | {{AIME box|year=2007|n=I|num-b=11|num-a=13}} | ||
Revision as of 12:40, 16 March 2007
Problem
In isosceles triangle 
, 
is located at the origin and 
is located at (20,0). Point 
is in the first quadrant with 
and angle 
. If triangle is rotated counterclockwise about point until the image of lies on the positive 
-axis, the area of the region common to the original and the rotated triangle is in the form 
, where 
are integers. Find 
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
The union of the area is equal to 
times the area of 
, minus the intersection of the area of the two triangles.
See also
| 2007 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
