An Equilateral triangle (ABC) is inscribed inside a circle. The side lengths of the triangle are 8 cm. What is the radius of the circle?

Answer 1

Let the triangle be named ABC.
Name the centre of the circle O, and the mid-point of BC, D.
Triangle ODC is a right-triangle, right-angled at D.
radius, r = OC
and OD=r/2 (∠OCD=30°).
DC=8cm/2=4 cm.
So all the sides ΔODC are known in terms of r.
Use Pythagoras theorem to solve for r:
(4cm)²+(r/2)²=r²