An equilateral triangle is circumscribed about a circle of radius 10sqrt3. What is the perimeter of the triangle?

In the above image equilateral triangle ABC is circumscribed about a circle with radius $= 10 \sqrt{3}$ units. Notice that the sides of the triangle are tangent to the circle, we draw a line segment from the center O to the vertex A, we also draw the radius OD. OA bisects angle A to two 30 degrees parts. And OD is perpendicular to AC.
$1 : \sqrt{3} : 2$ , hence: AD $= 10 \sqrt{3} \cdot \sqrt{3} = 30$ units. Since OD bisects AC, we conclude that each side of the triangle ABC is 60 units therefore the perimeter is $3 \cdot 60 = 180$ units.