An equilateral triangle with sides of length 6 is inscribed in a circle. what is the diameter of the circle? .

To solve for the diameter of the circle, we have to divide the triangle in to parts to solve for the radius. The angles of the triangle is 60 degrees. 

∠ACD is 60°
∠OCD is equal to ∠ACD / 2 which is 60/2 or 30 degrees.

In triangle OCD as shown in the picture attached,
 cos 30°= CD / OC
 √3 / 2   = 3 / r
  r = 3 x 2 /√3
     = 3.4641 cm

Therefore, the diameter is 6.93 cm.