1995 AMC 8 Problem 9
Attempt Problem 9 of the 1995 AMC 8 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 1995 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
9.
Three congruent circles with centers and are tangent to the sides of rectangle as shown. The circle centered at has diameter and passes through points and The area of the rectangle is
Answer: C
Small hint:
The diameter of each circle is so the short side of the rectangle equals
Big hint:
The long side spans two full diameters
Solution:
Each circle has diameter The short side of the rectangle equals one diameter, so it is
Since the circle at passes through and all three circles have radius and the long side spans two full diameters: The area is
Thus, the correct answer is C .
Problem 9 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
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