Difference between revisions of "1998 AHSME Problems/Problem 11"
(New page: == Problem == Let <math>R</math> be a rectangle. How many circles in the plane of <math>R</math> have a diameter both of whose endpoints are vertices of <math>R</math>? <math> \mathrm{(A)...) |
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Latest revision as of 13:29, 5 July 2013
Problem
Let 
be a rectangle. How many circles in the plane of have a diameter both of whose endpoints are vertices of ?
Solution
There are 
pairs of vertices of . However, both diagonals determine the same circle, therefore the answer is 
.
![[asy] 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-B)/2) ), red ); draw( circle( (C+B)/2, length((C-B)/2) ), red ); draw( circle( (C+D)/2, length((C-D)/2) ), red ); draw( circle( (A+D)/2, length((A-D)/2) ), red ); draw( circle( (A+B+C+D)/4, length((A-C)/2) ), green ); [/asy]](http://latex.artofproblemsolving.com/b/3/c/b3c7ec4213701f79433fd8a5b77812e1901048b9.png)
See also
| 1998 AHSME (Problems • Answer Key • Resources) | ||
| 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 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
