1983 AHSME Problems/Problem 2

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 $\boxed{\textbf{(B)} \ 2}$ .

1983 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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1983 AHSME Problems/Problem 2

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