Difference between revisions of "2021 Fall AMC 10B Problems/Problem 11"
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draw(A--B--C--D--E--F--cycle); | draw(A--B--C--D--E--F--cycle); | ||
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==Solution 2== | ==Solution 2== | ||
Revision as of 15:19, 24 November 2021
Contents
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 1
import olympiad; unitsize(50); Pair A,B,C,D,E,F,O; A = origin; B = (-0.5,0.866025); C=(0,1.7320508); D=(1,1.7320508); E=(1.5,0.866025); F=(1,0); draw(A--B--C--D--E--F--cycle); (Error making remote request. Unknown error_msg)
Solution 2
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 | ||
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