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 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

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