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too complicated to be written here. Click on the link to download a text file. 

X(1), X(2), X(5), X(6), X(54), X(378), X(4846) X(14389) = P = X(2)X(6) and X(5)X(49) excenters 

K502 is the cubic Ke1(X5) in CL054. K502 is an isogonal pivotal cubic with pivot P at the intersection of the lines X(2)X(6) and X(5)X(49). P is now X(14389) in ETC. It is also the root of K732. Let P be a point. Denote by Bc the intersection of AB with the parallel line to AC through P, by Cb the intersection of AC with the parallel line to AB through P. The other intersections Ca, Ac, Ab and Ba are defined cyclically. The Euler lines of PBcCb, PCaAc and PAbBa concur if and only if P lies on K502. See the related Q076. 
