Circles and Reflections in a Triangle: What is this about?
A Mathematical Droodle


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Explanation

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Copyright © 1996-2017 Alexander Bogomolny

I 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 Ka, Kb, and Kc denote the reflections in sides BC, AC, and AB, respectively. Then the circumcircles of four triangles ABC, AKcKb, BKaKc and CKbKa are concurrent.

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Copyright © 1996-2017 Alexander Bogomolny

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