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>?
 
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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<math>\text{(A)} \ 1 \qquad  \text{(B)} \ 2 \qquad  \text{(C)} \ 3 \qquad  \text{(D)} \ 4 \qquad  \text{(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>
 
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>

Revision as of 13:19, 27 June 2015

Problem

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

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

Solution

The points $3 \, \text{cm}$ away from $P$ can be represented as a circle with radius $3\,\text{cm}$. The maximum number of intersections between two circles is $\boxed{(\text{B}) \; 2}$

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