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.

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Alastair King   --   Mathematical Sciences   --   University of Bath Updated 31 Aug 2015