1986 AMC 12 Problem 28
Attempt Problem 28 of the 1986 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 1986 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
is a regular pentagon. and are the perpendiculars dropped from onto extended and extended, respectively. Let be the center of the pentagon. If then equals
Answer: C
Small hint:
Let be the side length and compute the pentagon’s area from its five central triangles
Big hint:
Also split the pentagon into triangles and with altitudes
Solution:
Let the side length be Since the apothem the five central triangles give pentagon area The same pentagon is the union of triangles and whose respective altitudes to side-length bases are Hence so Also Therefore
Thus the correct answer is C.
Problem 28 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
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- 1963 AMC 12
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