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Question -

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



Answer -

Let ABC be an equilateral triangle of side 9 cm and let AD be one of its medians. Let G be the centroid of . Then  

We know that in an equilateral triangle centroid coincides with the circumcentre. Therefore, G is the centre of the circumcircle with circumradius GA.
As per theorem, G is the centre and  . Therefore,
 
In  we have
 
Therefore radius AG = 

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