1983 AHSME Problems/Problem 2: Difference between revisions
Created page with "==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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==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>? | ||
<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 
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 with radius 
. The maximum number of intersections between two circles is 
