A few weeks ago a student and I noticed that if connect a point on a circle to the two endpoints of a diameter, you seem to get a right triangle. After working for a bit, we came up with pretty nice proof of why that is, in fact, the case. I told him that if he wrote it up, I’d post it on my blog.

Well, it just rolled into my inbox, and it’s quite a pretty explanation–he uses without proof facts we’d already proved: that the sum of the interior angles in a triangle add to 180 degrees, and that isosceles triangles (with two equal sides) also have two equal angles.

Without further ado, I present Gavin’s proof: