Question

An equilateral triangle of side 9cm is inscribed in a circle. 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 le Δ 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=AB^2+DB^2`

⇒`AD=sqrt(81-81/4)=(9sqrt3)/2cm`

`∴Radius = AG=2/3AD=3sqrt3cm`