Equidistance and Circles for Triangles (VIDEO!)
Is it obvious that for any three points one can draw a circle through them? That is, is it true that every triangle sits perfectly inside some circle with all three of its vertices on that circle? How about the other way round? Is there always a circle that sits inside a triangle touching each of its three sides?
We use equidistance to swiftly show that the answers to both of these questions is yes!