Let A'B'C' be the antimedial triangle, A”B”C” the intouch triangle. Let Ab, Ac be the intersections between B'C' and A”B”, A”C”. Define analogously Bc, Ba, Ca, Cb. The six points Ab, Ac, Bc, Ba, Ca, Cb lie in a conic (figure 1). The Euler lines of A”AbAc, B”BcBa, C”CaCb concur at the Feuerbach point F. Their parallels from A, B, C concur at the point X(80) and their parallels from A”, B”, C” concur at the antipodal of F in the incircle (figure 2).