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in Mathematics by (35.7k points)

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

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

Then AG : GD = 2:1 

WKT in an equilateral Δle centroid coincides with the circum center 

Therefore, G is the center of the circumference with circum radius GA 

Also G is the center and GD ⊥ BC . 

Therefore, 

In right triangle ADB, we have

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