An equilateral triangle with one side 6cm is inscribed in a circle with its three vertices on the circumference. What is the diameter of the circle?

Let's label the triangle's vertices A,B and C, and the center of the circle - O.

Find a midpoint between A and B, call it M. AOM will be a right triangle with one of the legs equal to 3 in length (since AM is half of AB). The angle OAM is equal to 30 degrees. The hypothenuse is the radius of the circle which we are trying to find.

As far as I recall there's an easy trig formula for finding the length of the hypothenuse if you know one of the angles and an adjacent leg. Just wish I remembered it :)

Posted by levik on 2002-06-03 18:27:43