2001 AMC 10 Problem 4

Below is the professionally curated solution for Problem 4 of the 2001 AMC 10, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2001 AMC 10 solutions, or check the answer key.

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Concepts:circle counting intersections

Difficulty rating: 1040

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

$2$

$3$

$4$

$5$

$6$

Solution:

Each side of the triangle is a segment, which can intersect a circle in at most $2$ points. With $3$ sides, the maximum is $3\cdot2=6$ points, and this is achievable.

Thus, the correct answer is E.

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