1970 AMC 12 Problem 27
Attempt Problem 27 of the 1970 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 1970 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
In a triangle, the area is numerically equal to the perimeter. What is the radius of the inscribed circle?
Answer: A
Small hint:
Express the area in terms of the inradius and semiperimeter
Big hint:
Use and perimeter
Solution:
If is the inradius and the semiperimeter, the triangle’s area is Its perimeter is The given equality yields Since we obtain
Therefore, the correct answer is A.
Problem 27 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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- 1961 AMC 12
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- 1963 AMC 12
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- 1969 AMC 12
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