2005 AMC 8 Problem 21
Attempt Problem 21 of the 2005 AMC 8 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 2005 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
How many distinct triangles can be drawn using three of the dots below as vertices?
Answer: C
Small hint:
There are dots total.
Big hint:
Subtract the choices of three collinear dots from all -dot choices.
Solution:
Notice that choosing any of these dots forms a triangle, except for the triples that form a straight line.
There are ways to choose the points, and then we subtract to get
Thus, C is the correct answer.
Problem 21 in other years
- 1985 AMC 8
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