Posted by Katy on .
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?

geometry 
MathMate,
Let the triangle be named ABC.
Name the centre of the circle O, and the midpoint of BC, D.
Triangle ODC is a righttriangle, rightangled 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