The Begonia Point

Let ABC be a triangle and let P be a point. Let A'B'C' be the Cevian triangle of P, which means that A', B', and C' are the intersections of AP, BP, and CP with BC, CA, and AB, respectively. Let X, Y, and Z be the reflections of P in B'C', C'A', and A'B', respectively. Then AX, BY, and CZ are concurrent. The name "begonia point" has been suggested for this point of concurrency.