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

Explanation

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 ABC. 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.