Find the radius of the circle that circumscribes an equilateral triangle of side 6 cm.

We know that in an equilateral triangle, centroid, orthocentre, circumcentre, and incentre are all the same point. Let’s assume O is this point for triangle ABC.
So, AD is perpendicular to BC and bisects it as well. Also, O divides AD in the ratio 2:1.
=> $$AD^2 = AC^2 - DC^2 = 36-9 = 27$$.
So, $$AD=3\sqrt{3}$$
Since, O divides AD in the ratio 2:1, AO will be $$2\sqrt{3}$$ which is the radius of the circle.
Thus, D is the correct answer.