Circles and Reflections in a Triangle: What is this about?
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Explanation
Copyright © 1996-2008 Alexander Bogomolny
I found the following fact in D. Wells' Curious and Interesting Geometry
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Let P be a point in the plane of a , Kb , and Kc denote the reflections in sides BC, AC, and AB, respectively. Then the circumcircles of four triangles ABC, AKc Kb , BKa Kc and CKb Ka are concurrent.
Copyright © 1996-2008 Alexander Bogomolny
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ABC. 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.
