HYACINTHOS 1535

> Are the Euler Lines of the triangles M11M12M13, M21M22M23, M31M32M33

concurrent?

 

Yes. At:

 

   Z= (4*cos(A)^4+(4*cos(B-C)^2-1)*cos(A)^2+cos(B-C)*(4*cos(A)+cos(B-C)))*cos(B-C)*sin(A)^2 : : (tri.)

     =  (5,51) /\ (154,157)

     = ( -6.313015585454211, 2.25428471766879, 4.993705332192548 )

 

César Lozada

 

 

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 Antreas P. Hatzipolakis

 

Let ABC be a triangle and A'B'C' the cevian triangle of O.

Denote:

Lb, Lc = the reflections of the AA' line in AB,AC, resp.

Ab, Ac = the orthogonal projections of A' on Lb,Lc, resp.

Similarly Bc,Ba and Ca,Cb.

Denote:

M11,M21,M31 = the midpoints of AbAc, BcBa, CaCb, resp.

M12,M22,M32 = the midpoints of BaCa, CbAb, AcBc, resp.

M13,M23,M33 = the midpoints of BcCb, CaAc, AbBa, resp.

Are the Euler Lines of the triangles M11M12M13, M21M22M23, M31M32M33

concurrent?

APH