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$A, B, C$ are points on $\odot O$ such that $\triangle A B C$ is equilateral. If the radius of the circle is $6,$ what is the perimeter of $\triangle A B C ?$...

Question

$A, B, C$ are points on $\odot O$ such that $\triangle A B C$ is equilateral. If the radius of the circle is $6,$ what is the perimeter of $\triangle A B C ?$

$A, B, C$ are points on $\odot O$ such that $\triangle A B C$ is equilateral. If the radius of the circle is $6,$ what is the perimeter of $\triangle A B C ?$



Answers

In Circle $O$ above with radius $r, \overline{A B}$ and $\overline{C D}$ are a pair of
perpendicular diameters. If the area and perimeter of square
$A D B C($ not shown $)$ are $a$ square inches and $b$ inches,
respectively, and if $a=b,$ what is the length, in inches, of $r ?$
$$\begin{array}{l}{\text { (A) } \sqrt{2}} \\ {\text { (B) } 2} \\ {\text { (C) } 2 \sqrt{2}} \\ {\text { (D) } 4 \sqrt{2}}\end{array}$$


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