¶ 2018 AMC8 Problem 23
¶ nan
Problem:
From a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the probability that at least one of the sides of the triangle is also a side of the octagon?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
For each side of the octagon, there are triangles containing that side. Because the triangles containing two adjacent sides of the octagon are counted twice, there are a total of triangles sharing a side with the octagon. The total number of triangles that can be formed from the eight vertices is , so the probability is = .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions