Difference between revisions of "2021 Fall AMC 10B Problems/Problem 11"
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A regular hexagon of side length <math>1</math> is inscribed in a circle. Each minor arc of the circle | A regular hexagon of side length <math>1</math> is inscribed in a circle. Each minor arc of the circle | ||
determined by a side of the hexagon is reflected over that side. What is the area of the region | determined by a side of the hexagon is reflected over that side. What is the area of the region | ||
Revision as of 22:03, 23 November 2021
Problem 11
A regular hexagon of side length 
is inscribed in a circle. Each minor arc of the circle
determined by a side of the hexagon is reflected over that side. What is the area of the region
bounded by these 
reflected arcs?
Solution
Let the hexagon described be of area 
and let the circle's area be 
.
Let the area we want to aim for be 
.
Thus, we have that 
, or 
.
By some formulas, 
and 
.
Thus, 
or 
.
~Hefei417, or 陆畅 Sunny from China
See Also
| 2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
