Let ABC be an equilateral triangle of side 9 cm.

And AD be one of its medians.

Then,

ADBC

BD = (1/2) BC

⇒ BD = (1/2) 9 = 4.5 cm

In triangle ADB,

AD² = AB² - BD²

⇒ AD² = 9² – (9/2)²

⇒ AD² = 81 – (81/4)

⇒ AD = (9√3)/2

In an equilateral triangle the centroid and circumcenter coincide and AO: OD = 2: 1

∴ radius AO = (2/3) AD

= (2/3) (9√3)/2

= 3√3 cm

Hence, radius of circle = 3√3 cm.