Posted by Katy on Tuesday, March 29, 2011 at 10:48pm.
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, Wednesday, March 30, 2011 at 9:14am
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
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