Difference between revisions of "2001 AMC 10 Problems/Problem 4"
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What is the maximum number of possible points of intersection of a circle and a triangle? | 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 | + | <math> \textbf{(A) }2\qquad\textbf{(B) }3\qquad\textbf{(C) }4\qquad\textbf{(D) }5\qquad\textbf{(E) }6 </math> |
== Solution == | == Solution == | ||
Revision as of 12:06, 16 March 2011
Problem
What is the maximum number of possible points of intersection of a circle and a triangle?
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 
points, but what if the circle was bigger? Then, each side would intersect the circle at 2 points.
Therefore, 
.
