1988 AMC 12 Problem 27
Attempt Problem 27 of the 1988 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 1988 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 the figure, and is tangent to the circle with center and diameter In which one of the following cases is the area of an integer?
Answer: D
Small hint:
Let the tangent point be and use the diameter to form a rectangle inside the trapezoid
Big hint:
Power of point relates half of to and
Solution:
The tangent point is the midpoint of and the tangent-secant relation gives Thus and the trapezoid area is Only makes the product under the radical a square; the area is
Thus the correct answer is D.
Problem 27 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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