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.
