1987 AMC 8 Problem 22
Attempt Problem 22 of the 1987 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1987 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
is a rectangle, is the center of the circle, and is on the circle. If and then the area of the shaded region is between which two values?
and
and
and
and
and
Answer: D
Small hint:
The diagonal is the radius; find it with the Pythagorean theorem
Big hint:
The shaded region is a quarter of the circle with the rectangle removed:
Solution:
Since and the diagonal which is the radius.
The shaded region is the quarter circle at minus the rectangle:
This lies between and
Thus, the correct answer is D .
Problem 22 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
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