Difference between revisions of "1983 AHSME Problems/Problem 2"

Problem

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

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

Solution

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