1952 AMC 12 Problem 27
Attempt Problem 27 of the 1952 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 1952 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
The ratio of the perimeter of an equilateral triangle having an altitude equal to the radius of a circle, to the perimeter of an equilateral triangle inscribed in the circle is:
Answer: E
Small hint:
Express each equilateral triangle’s side length in terms of the same circle radius
Big hint:
An equilateral triangle of altitude has side , while an inscribed one has side
Solution:
An equilateral triangle with side has altitude Thus the first triangle has side and perimeter An equilateral triangle inscribed in a circle of radius has side and perimeter
The perimeter ratio is therefore so the correct answer is E.
Problem 27 in other years
- 1950 AMC 12
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