Difference between revisions of "1960 AHSME Problems/Problem 12"
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Revision as of 19:13, 10 May 2018
Problem 12
The locus of the centers of all circles of given radius 
, in the same plane, passing through a fixed point, is:
Solution
![[asy] draw(circle((0,0),50)); dot((0,0)); dot((-30,-40)); draw(circle((-30,-40),50),dotted); dot((50,0)); draw(circle((50,0),50),dotted); draw((-30,-40)--(0,0)--(50,0)); [/asy]](http://latex.artofproblemsolving.com/b/6/c/b6c605c33f731b8604029add8049ce1c86ec143e.png)
If a circle passes through a point, then the point is units away from the center. That means that all of the centers are units from the point. By definition, the resulting figure is a circle, so the answer is 
.
See Also
| 1960 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
