### Circles and Reflections in a Triangle: What is this about?

A Mathematical Droodle

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Copyright © 1996-2017 Alexander BogomolnyI found the following fact in D. Wells' *Curious and Interesting Geometry* (Penguin Books, 1991, p 258.)

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Let P be a point in the plane of ΔABC. Reflect P in the side lines of the triangle and let K_{a}, K_{b}, and K_{c} denote the reflections in sides BC, AC, and AB, respectively. Then the circumcircles of four triangles ABC, AK_{c}K_{b}, BK_{a}K_{c} and CK_{b}K_{a} are concurrent.

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Copyright © 1996-2017 Alexander Bogomolny61256652 |