Difference between revisions of "1983 AHSME Problems/Problem 2"
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==Problem== | ==Problem== | ||
| − | Point <math>P</math> is outside circle <math>C</math> on the plane. At most how many points on <math>C</math> are <math>3 \ | + | Point <math>P</math> is outside circle <math>C</math> on the plane. At most how many points on <math>C</math> are <math>3 \ \text{cm}</math> from <math>P</math>? |
| − | <math>\ | + | <math>\textbf{(A)} \ 1 \qquad \textbf{(B)} \ 2 \qquad \textbf{(C)} \ 3 \qquad \textbf{(D)} \ 4 \qquad \textbf{(E)} \ 8</math> |
==Solution== | ==Solution== | ||
| − | The points <math>3 \ | + | The points <math>3 \ \text{cm}</math> away from <math>P</math> can be represented as a circle centered at <math>P</math> with radius <math>3 \ \text{cm}</math>. The maximum number of intersection points of two circles is <math>\boxed{(\text{B}) \; 2}</math> |
==See Also== | ==See Also== | ||
{{AHSME box|year=1983|num-b=1|num-a=3}} | {{AHSME box|year=1983|num-b=1|num-a=3}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 16:58, 26 January 2019
Problem
Point 
is outside circle 
on the plane. At most how many points on are 
from ?
Solution
The points away from can be represented as a circle centered at with radius . The maximum number of intersection points of two circles is 
See Also
| 1983 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 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. 
