FidgetBoss 4000's 2019 Mock AMC 12B Problems/Problem 3
Revision as of 15:03, 19 November 2020 by Icematrix2 (talk | contribs) (Created page with "==Problem== There are <math>\binom{8}{4}=70</math> distinct quadrilaterals that can be formed from the vertices of a regular octagon. Which of these statements must hold true...")
Problem
There are distinct quadrilaterals that can be formed from the vertices of a regular octagon. Which of these statements must hold true for all those quadrilaterals?
Solution
All regular octagons can be inscribed in a circle, thus any subset of vertice's from this octagon also all lie on the same circle. It is easy to see that none of the other answer choices work. Therefore, the answer is $\boxed{\textbf{(B) }\text{All of the 70 quadrilaterals are cyclic.}}
See also
FidgetBoss 4000's 2019 Mock AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 2 |
Followed by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by FidgetBoss 4000's Mock American Mathematics Competitions.