If radius of the circumcircle of an equilateral triangle is 8 cm; then the measure of radius of its incircle is:

4 cm

Radius of circumcircle = \(\frac{a}{\sqrt {3}}\) = 8

and radius of incircle = \(\frac{a}{2 \sqrt {3}}\)

Therefore, radius of incircle = \(\frac{8}{2}\) = 4 cm

Or

Note: In equilateral triangle the ratio of circumradius to inradius is 2 : 1.

Therefore,

If Circumradius = 8 cm, then inradius = 4cm