Let ABC be a triangle, H is the orthocenter of the triangle ABC. Denote A1,B1,C1 lie on HA,HB,HC. Such that HA1/HA=HB1/HB=HC1/HC=k. d*a be the line through A1 and parallel with Euler line meet AB,AC at A*b, A*c respectively. Define B*a,B*c,C*a, C*b cyclically. A2B2C2 is the triangle created by the Euler line of three triangles AAbAc, BBcBa,CCaCb.
1-A*2B*2C*2 and ABC are two similar triangle, and them have the same Euler line
2-A*2B*2C*2 are perpective with ABC, the perpector be a point lie on Euler line, if k=0 then the perpector is Gossard perspector
3-Reflection of thee lines d*a,d*b,d*c in BC,CA,AB respectively are concurrent be a point lie on the X(3)X(110)
4-d*a also is the Euler line of the triangle with a vertex is A, two line AB,AC, and A1 is the orthocenter, (d*b,d_c similar)

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