2005 AMC 8 Problems/Problem 25
Contents
Problem 25
A square with side length 2 and a circle share the same center. The total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square. What is the radius of the circle?
Solutions
Solution 1
Let the region within the circle and square be . In other words, it is the area inside the circle the square. Let be the radius. We know that the area of the circle minus is equal to the area of the square, minus .
We get:
So the answer is .
Solution 2
We realize that since the areas of the regions outside of the circle and the square are equal to each other, the area of the circle must be equal to the area of the square.
So the answer is .
Video Solution by OmegaLearn
https://youtu.be/abSgjn4Qs34?t=2763
Video Solution
https://www.youtube.com/watch?v=xdeWCR666q8
See Also
2005 AMC 8 (Problems • Answer Key • Resources) | ||
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