Difference between revisions of "2017 UNCO Math Contest II Problems/Problem 2"
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== Problem == | == Problem == | ||
| + | <asy> | ||
| + | |||
| + | pair A=dir(60),B=dir(120),C=dir(180),D=dir(240),E=dir(300),F=dir(360),O=(0,0); | ||
| + | pair G=(2/sqrt(3))*A,H=(2/sqrt(3))*B,I=(2/sqrt(3))*C,J=(2/sqrt(3))*D,K=(2/sqrt(3))*E,L=(2/sqrt(3))*F; | ||
| + | draw(circle(O,1),black); | ||
| + | draw(A--B--C--D--E--F--A); | ||
| + | draw(G--H--I--J--K--L--G); | ||
| + | |||
| + | </asy> | ||
| + | |||
| + | Find the ratio of the area of a regular hexagon circumscribed | ||
| + | around a circle to the area of a regular | ||
| + | hexagon inscribed inside the same circle. (A polygon | ||
| + | is called regular if all its sides are the same length and | ||
| + | all its corner angles have the same measure. A hexagon | ||
| + | is a polygon with six sides.) | ||
== Solution == | == Solution == | ||
Revision as of 00:13, 20 May 2017
Problem
![[asy] pair A=dir(60),B=dir(120),C=dir(180),D=dir(240),E=dir(300),F=dir(360),O=(0,0); pair G=(2/sqrt(3))*A,H=(2/sqrt(3))*B,I=(2/sqrt(3))*C,J=(2/sqrt(3))*D,K=(2/sqrt(3))*E,L=(2/sqrt(3))*F; draw(circle(O,1),black); draw(A--B--C--D--E--F--A); draw(G--H--I--J--K--L--G); [/asy]](http://latex.artofproblemsolving.com/2/4/1/241880254b71b42a37a3e4049a5c90b55eea4397.png)
Find the ratio of the area of a regular hexagon circumscribed around a circle to the area of a regular hexagon inscribed inside the same circle. (A polygon is called regular if all its sides are the same length and all its corner angles have the same measure. A hexagon is a polygon with six sides.)
Solution
See also
| 2017 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
