MHB Problem of the week #34 - November, 19th 2012

[Jameson]

In the above circle the radius is 6 and chord $AB=6$. What is the area of the shaded region?
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[Jameson]

Congratulations to the following members for their correct solutions:

1) MarkFL
2) SuperSonic4
3) soroban
4) Sudharaka
5) BAdhi
6) caffeinemachine

Solution (from soroban):
[sp]Let $O$ be the center of the circle.

The area of sector $AOB \text{ }$ is: .[/color]$\frac{1}{6}\pi r^2 \:=\:\frac{\pi}{6}(6^2) \:=\:6\pi$

The area of equilateral triangle $AOB \text{ }$ is: .[/color]$\frac{\sqrt{3}}{4}(6^2) \:=\:9\sqrt{3}$

Therefore, area of the segment is: .[/color]$6\pi - 9\sqrt{3} \;\approx\;3.261$
[/size][/sp]