If the circumradius of an equilateral triangle ABC be 8 cm, then the height of the triangle is

Let ABC be the equilateral triangle and O be the circumcentre. AO extended meet BC at D.

In an equilateral triangle, the centroid, orthocentre, incentre and circumcentre, all lie on the same point, => the median and height are the same lines.

=> O is also the centroid of the triangle.

Since, the centroid divides the median in the ratio 2 : 1

It is given that OA = 8 cm

=> Height AD = $$8 * \frac{3}{2}$$ = 12 cm