Circles, Triangles and Reflections : the Ballerina's Theorem.

I have given an RIBBM Masterclass
with this title at Bath.
The class was based on the classical theorem that
the circumcircle of a triangle consists of precisely those points
whose reflections in the three sides are colinear.
For the purposes of presentation, I christened this "the ballerina's theorem",
since it tells a ballerina where to stand if she wants to line up her
reflections in three practice mirrors.