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 \, \text{cm}</math> from <math>P</math>?
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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</math> cm from <math>P</math>?
  
<math>\text{(A)} \ 1 \qquad  \text{(B)} \ 2 \qquad  \text{(C)} \ 3 \qquad  \text{(D)} \ 4 \qquad  \text{(E)} \ 8</math>
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<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 \, \text{cm}</math> away from <math>P</math> can be represented as a circle with radius <math>3\,\text{cm}</math>. The maximum number of intersections between two circles is <math>\boxed{(\text{B}) \; 2}</math>
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The points <math>3</math> cm away from <math>P</math> can be represented as a circle centered at <math>P</math> with radius <math>3</math> cm. The maximum number of intersection points of two circles is <math>\boxed{\textbf{(B)} \ 2}</math>.
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==See Also==
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{{AHSME box|year=1983|num-b=1|num-a=3}}
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{{MAA Notice}}

Latest revision as of 00:39, 20 February 2019

Problem

Point $P$ is outside circle $C$ on the plane. At most how many points on $C$ are $3$ cm from $P$?

$\textbf{(A)} \ 1 \qquad  \textbf{(B)} \ 2 \qquad  \textbf{(C)} \ 3 \qquad  \textbf{(D)} \ 4 \qquad  \textbf{(E)} \ 8$

Solution

The points $3$ cm away from $P$ can be represented as a circle centered at $P$ with radius $3$ cm. The maximum number of intersection points of two circles is $\boxed{\textbf{(B)} \ 2}$.

See Also

1983 AHSME (ProblemsAnswer KeyResources)
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


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