2001 AMC 10 Problem 4

Attempt Problem 4 of the 2001 AMC 10 below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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

$2$

$3$

$4$

$5$

$6$

Answer: E

Concepts:circle counting intersections

Difficulty rating: 1040

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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