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2001 AMC 10 Problems/Problem 4

Revision as of 12:06, 16 March 2011 by Pidigits125 (talk | contribs) (→‎Problem)

Problem

What is the maximum number of possible points of intersection of a circle and a triangle?

$\textbf{(A) }2\qquad\textbf{(B) }3\qquad\textbf{(C) }4\qquad\textbf{(D) }5\qquad\textbf{(E) }6$

Solution

Here is the picture: http://www.artofproblemsolving.com/Forum/download/file.php?id=6658&

We can draw a circle and a triangle, such that each side is tangent to the circle. This means that each side would intersect the circle at one point.

You would then have $3$ points, but what if the circle was bigger? Then, each side would intersect the circle at 2 points.

Therefore, $2 \times 3 = \boxed{\textbf{(E) }6}$.

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