1965 AMC 12 Problem 2
Attempt Problem 2 of the 1965 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 1965 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
2.
A regular hexagon is inscribed in a circle. The ratio of the length of a side of the hexagon to the length of the shorter of the arcs intercepted by the side is:
Answer: D
Small hint:
Each side of an inscribed regular hexagon equals the circle’s radius
Big hint:
The shorter arc is one sixth of the circumference
Solution:
If the radius is the hexagon side is Its intercepted minor arc has length The ratio is
Therefore, the correct answer is D.
Problem 2 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
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- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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