Question

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

Answer 1

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
(AB)2 =(AD)2+( DB)2
(9)2=(AD)2+(DB)2
=AD=3ROOT3CM