2023 AMC 8 Problem 12
Attempt Problem 12 of the 2023 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2023 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
12.
The figure below shows a large unshaded circle with a number of smaller unshaded and shaded circles in its interior. What fraction of the interior of the large unshaded circle is shaded?
Answer: B
Small hint:
Circle areas are proportional to the square of the radius
Big hint:
Count shaded area in units of the smallest circle’s area
Video solution:
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Written solution:
Let each smallest circle have radius
This means that there are shaded unit circles, which total to area.
There is also a shaded circle with radius with two unshaded circles of radius inside.
This gives us an extra shaded area of
The total shaded area is The area of the large unshaded circle is Therefore, the desired fraction is
Thus, B is the correct answer.
Problem 12 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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