1968 AMC 12 Problem 30
Attempt Problem 30 of the 1968 AMC 12 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 1968 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
30.
Convex polygons and are drawn in the same plane with and sides, respectively, If and do not have any line segment in common, then the maximum number of intersections of and is:
none of these
Answer: A
Small hint:
A line segment can enter and leave a convex polygon at most once
Big hint:
Apply that bound to each side of the polygon with fewer sides
Solution:
Each side of lies on a line, and its intersection with the convex region is a single segment or empty. Thus that side crosses the boundary of at most twice. Across sides there are at most and a suitable thin convex -gon crossing a convex -gon attains this bound.
Therefore, the correct answer is A.
Problem 30 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
- 1960 AMC 12
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