An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.

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


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