# 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 14:19, 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