An equilateral tr

Let ABC be an equilateral triangle of side 9 cm

Let, AD be one of its medians and G be the centroids of the triangle ABC

Then,

AG: GD = 2: 1

We know that,

In an equilateral triangle centroid coincides with the circumcentre

Therefore,

G is the centre of the circumference with circum radius GA

Also, G is the centre and GD is perpendicular to BC

Therefore,

In right triangle ADB, we have

AB² = AD² + DB²

9² = AD² + DB²

AD = cm

Therefore,

Radius = AG = AD

= 3 cm