2002 AMC 10B Problems/Problem 18

Problem

Four distinct circles are drawn in a plane. What is the maximum number of points where at least two of the circles intersect?

$\textbf{(A) } 8\qquad \textbf{(B) } 9\qquad \textbf{(C) } 10\qquad \textbf{(D) } 12\qquad \textbf{(E) } 16$

Solution

We know that $2$ distinct circles can intersect at no more than $2$ points. Thus $4$ circles can intersect at $2 \times 4= \boxed{\textbf{(D)}\ 8}$ points total.

Page

Toolbox

Search

2002 AMC 10B Problems/Problem 18

Problem

Solution