There is a triangle ABC on a euclidean plane. Like every other triangle on the plane, it follows the law of sines, that is, BC/sin(A) = AC/sin(B) = AB/sin(C).

So we know that these three numbers are equal to one another, but most people don't know that they are also equal to the length of a special line segment. What is the significance of this length, and can you prove it?

Just looking at a right triangle, and guessing at a possible generalization, the three terms might be equal to:

The diameter of the circle into which the triangle is inscribed.

Posted by Rollercoaster on 2005-12-13 11:39:44