A generalization of Gossard perspector and X(110)

Geometry Level pending

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. da be the line through A1 and parallel with Euler line meet AB,AC at Ab, Ac respectively. Define Ba,Bc,Ca, Cb cyclically. A2B2C2 is the triangle created by the Euler line of three triangles AAbAc, BBcBa,CCaCb. 1-A2B2C2 and ABC are two similar triangle, and them have the same Euler line 2-A2B2C2 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 da,db,dc in BC,CA,AB respectively are concurrent be a point lie on the X(3)X(110) 4-da also is the Euler line of the triangle with a vertex is A, two line AB,AC, and A1 is the orthocenter, (db,d_c similar)

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