2025 AMC 8 Problems/Problem 18
Solution
The area of the shaded region in the circle on the left is the area of the circle minus the area of the square, or . The shaded area in the circle on the right is
of the area of the circle minus the area of the square, or
, which can be factored as
. Since the shaded areas are equal to each other, we have
, which simplifies to
. Taking the square root, we have
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