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1998 AHSME Problems/Problem 11

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Problem

Let R be a rectangle. How many circles in the plane of R have a diameter both of whose endpoints are vertices of R?

\mathrm{(A) \ }1 \qquad \mathrm{(B) \ }2 \qquad \mathrm{(C) \ }4 \qquad \mathrm{(D) \ }5 \qquad \mathrm{(E) \ }6

Solution

There are 6 pairs of vertices of R. However, both diagonals determine the same circle, therefore the answer is \boxed{5}.

size(200);defaultpen(0.8);pair A=(0,0), B=(5,0), C=(5,2), D=(0,2);draw ( A--B--C--D--cycle );draw( circle( (A+B)/2, length((A...

See also

1998 AHSME (Problems)
Preceded by
Problem 10 		Followed by
Problem 12
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
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