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 $P$ ?

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

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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1983 AHSME Problems/Problem 2

Problem

Solution