2002 AMC 8 Problem 1
Attempt Problem 1 of the 2002 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 2002 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
1.
A circle and two distinct lines are drawn on a sheet of paper. What is the largest possible number of points of intersection of these figures?
Answer: D
Small hint:
Count each type of pair of figures separately.
Big hint:
Each line can meet the circle at most twice, and the two lines can meet once.
Solution:
A line and a circle can intersect at no more than two points, and two distinct lines can intersect at no more than one point.
Arrange the two lines so each meets the circle twice and the two lines meet at a different point. This gives
Thus, D is the correct answer.
Problem 1 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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