2004 AMC 12A Problems/Problem 24
Problem 24
A plane contains points and with . Let be the union of all disks of radius in the plane that cover . What is the area of ?
Solution
As the red circles move about segment , they cover the area we are looking for. On the left side, the circle must move around pivoted on . On the right side, the circle must move pivoted on However, at the top and bottom, the circle must lie on both A and B, giving us our upper and lower bounds.
This egg-like shape is .
The area of the region can be found by dividing it into several sectors, namely
See also
2004 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 23 |
Followed by Problem 25 |
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