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

Explanation

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I found the following fact in D. Wells' Curious and Interesting Geometry (Penguin Books, 1991, p 258.)

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_cK_b, BK_aK_c and CK_bK_a are concurrent.

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