Question

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

Answer 1

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 = $\frac{2}{3}AD=3\sqrt{3}\mathrm{cm}$