a geometric observation

I've been spending a lot of time thinking about centers of triangles recently -- they're fascinating. Here's a recent observation about circumcenters (the point of concurrency of the perpendicular bisectors of a triangle):

The measure of the angle formed by constructing segments from two vertices of a triangle to its circumcenter is twice the measure of the angle at the third vertex.

In other words, given ∆ABC with circumcenter H, m∠AHB = 2(m∠ACB).

A proof? Think about circumscribing a circle about the triangle; the circumcenter of the triangle is the center of that circle...