Difference between revisions of "FidgetBoss 4000's 2019 Mock AMC 12B Problems/Problem 3"
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==Solution== | ==Solution== | ||
| − | All regular octagons can be inscribed in a circle, thus any subset of <math>4</math> 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 | + | All regular octagons can be inscribed in a circle, thus any subset of <math>4</math> 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 <math>\boxed{\textbf{(B) }\text{All of the 70 quadrilaterals are cyclic.}}</math> |
==See also== | ==See also== | ||
Latest revision as of 16:04, 19 November 2020
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 
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. 
