Date: Fri, 28 Jul 2000 23:55:19 EDT
I am not a student. A smart ass friend of mine posed this question to me as a challenge and for the life of me, I can't remember how to do it.
I assume this is a high school level question. I am an adult (25).
Here is the question:
Join each vertex of the triangle to the center of the circle to form three, congruent isosceles triangles. Condider one of these tringles, the one I have shaded green in the diagram.
The angle in this triangle at the center of the circle has measure 360o/3 = 120o. The sum of the angles in any triangle is 180o hence each of the other angles in this triangle has measure (180o - 120o)/2 = 30o.
Drop a perpendicular from the vertex of this triangle (center of the circle) to the side of length 12 to form a triangle PQR. |QR| = 12/2 = 6, angle QRP is 30o and RP is the radius of the circle. You should now be able to find |RP| and then calculate the circumference of the circle.Cheers,