Perimeter of a triangle inscribed in a circle

[Fedcer]

Homework Statement

Find the Perimeter of an equilateral triangle inscribed in a circle knowing the radius r.

Homework Equations

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The Attempt at a Solution

Browsing the web I found that the intersection of the three perpendicular bisectors of a traingle is the center of it's circumscribed circle. Knowing this I proceeded as following: [img=http://img214.imageshack.us/img214/2971/problem1bgc6.th.jpg]
I think that what I did is correct. However, since I should've been able to solve it with what I already knew I thought that maybe there is another easier solution.

Thanks.

 

[jing]

Triangle AOB is isoceles. Just drawing the perpendicular from O to AB get you to the same position as the result you quote ( in fact it demonstrates it)