Answer :


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.


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