1996 AMC 8 Problem 25
Attempt Problem 25 of the 1996 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 1996 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
25.
A point is chosen at random from within a circular region. What is the probability that the point is closer to the center of the region than it is to the boundary of the region?
Answer: A
Small hint:
A point is closer to the center than the boundary exactly when its distance from the center is less than half the radius
Big hint:
Compare the area of the inner circle of radius to the whole circle of radius
Solution:
Take the radius to be A point at distance from the center is closer to the center than to the boundary when i.e.
The favorable region is a circle of radius with area out of the total area The probability is
Thus, the correct answer is A .
Problem 25 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
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