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2001 AMC 10 Problem 4

Problem 4 of 25EasierGeometryCounting & Probability

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

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Solution

Each side of the triangle is a segment, which can intersect a circle in at most 22 points. With 33 sides, the maximum is 3⋅2=63\cdot2=6 points, and this is achievable. Thus, the correct answer is E.

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Concepts: circle · counting intersections

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.