1984 AMC 12 Problem 26
Attempt Problem 26 of the 1984 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 1984 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
26.
In the obtuse triangle If the area of is then the area of is
not uniquely determined
Answer: B
Small hint:
Draw segment and compare with
Big hint:
Those triangles have the same base and equal altitudes; also is the midpoint of
Solution:
Draw Since points and have equal perpendicular distances from so Therefore Because is the midpoint of triangle has half the area of Thus
Therefore, the correct answer is B.
Problem 26 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
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- 1954 AMC 12
- 1955 AMC 12
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