HYACINTHOS 25081

[Antreas P. Hatzipolakis]:

 

Let ABC be a triangle.

Denote:

A', B', C' =the reflections of N in BC, CA, AB, resp.

A", B", C" = the reflections of A, B, C in B'C', C'A', A'B', resp.

The circles NAA", NBB", NCC" ae coaxial.

Which is the other than N point of concurrence?

 

[César Lozada]:

 

Z = Antigonal conjugate of X(1157)

= (2*SA-3*R^2)/(SA^2-R^2*SA-S^2) : :  (barycentrics)

= (4*cos(A)*cos(B-C)+2*cos(2*A)- 1)/(2*cos(2*A)*cos(B-C)+cos(3* A)) : : (trilinears)

= On cubics K060, K067, K464 and these lines: {5,195}, {30,5684}, {143,11538},{2070,6343}

= [ 0.070174691480038, 0.07204991260831, 3.558395454033995 ]

 

César Lozada