HYACINTHOS 21922

X(5446) = INTERSECTION OF LINES X(371)X(5417) AND X(372)X(5419)


Coordinates (pending)



The first attempt was done intersecting lines X(371)X(5417) and
X(372)X(5419).

This produced the not nice trilinears

G(A,B,C) : G(B,C,A) : G(C,A,B)

where G(A,B,C)=

(4-4*cos(2*B)+cos(2*B-2*C)-4*cos(2*C)+5*cos(2*A))*(2*cos(B-C)*(-1+cos(2*A))+
2*cos(A))*(2*cos(B-C)*(3-2*cos(2*A)+sin(2*A))+cos(A)-cos(3*A)+6*sin(A))*(-2*
cos(B-C)*(-3+2*cos(2*A)+sin(2*A))+cos(A)-cos(3*A)-6*sin(A))

Using this center function it was possible to determine that X(5446) is also
on lines X(3)X(51) and X(4)X(52).


With these last two lines it is possible to find a nicer expression for
trilinears of X(5446)

F(A,B,C) : F(B,C,A) : F(C,A,B),

where F(A,B,C) =cos(2*A)*cos(B-C) - 2*cos(B)*cos(C)



X(5447) = COMPLEMENT OF X(5446)


Coordinates (pending)



Trilinears: F(A,B,C) : F(B,C,A) : F(C,A,B)

where F(A,B,C)=cos(A)*( cos(2*B) + cos(2*C) - 3)



Regards

Cesar Lozada