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 360^{o}/3 = 120^{o}. The sum of the angles in any triangle is 180^{o} hence each of the other angles in this triangle has measure (180^{o}  120^{o})/2 = 30^{o}. 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 30^{o} 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,Penny
