Consider △ABC as an equilateral triangle with side 9 cmTake AD as one of its medianWe know thatAD⊥BCIt can be written asBD=21​×BCBy substituting the valuesBD=21​×9So we getBD=4.5 cmConsider △ADBUsing the Pythagoras theoremAB2=AD2+BD2Substituting the values92=AD2+(9/2)2On further calculationAD2=92−(29​)2So we getAD2=81−481​By taking out the square rootAD=293​​ cmWe know that the centroid and circumcenter coincide in an equilateral triangleAG:GD=2:1The radius can be written asAG=32​ ADBy substituting the valuesAG=32​×293​​So we getAG−33​ cmTherefore the radius of the circle is 33​ cm