HYACINTHOS 21900

Dear geometers:


Here are two coordinates pending in ETC.


Maybe this information may be of interest for Professor Kimberling.


Regards


César Lozada.



X(5415) = 4th KENMOTU HOMOTHETIC CENTER


Trilinears (pending)

The A'B'C' defined at X(5412) is homothetic to the extangents triangle, and
the center of homothety is X(5415). Also, X(5415) = {X(6), X(55)}-harmonic
conjugate of X(5416). (Randy Hutson, February 9, 2013)

The coordinates of X(5415) are:

Trilinears: a*( (2*R + r ) + (s-a) ) : :

Trilinears: f(A) : f(B) : f(C) , where f(A)=( (2*R + r + s)/R - 2*sin(A)) *
sin(A)

Barycentrics f(A)*sin(A) : f(B)*sin(B) : f(C)*sin(C)



ETC SEARCH : 1.246310683967065.., 1.64076433091358.., 1.929530398674793..



X(5415) is a major center.

X(5415) lies on lines : X(6)-X(31), X(19)-X(5412) , X(40)-X(371)



X(5416) = 5th KENMOTU HOMOTHETIC CENTER


Trilinears (pending)

The A'B'C' defined at X(5413) is homothetic to the extangents triangle, and
the center of homothety is X(5415). Also, X(5416) = {X(6), X(55)}-harmonic
conjugate of X(5416). (Randy Hutson, February 9, 2013)

The coordinates of X(5416) are:

Trilinears: a*( (2*R + r ) – (s-a) ): :

Trilinears: f(A) : f(B) : f(C) , where f(A) = ( (2*R + r - s)/R +
2*sin(A))*sin(A)

Barycentrics f(A)*sin(A) : f(B)*sin(B) : f(C)*sin(C)



ETC SEARCH : 0.626431598880468.., 1.27040179200258.., 2.472033272576223..

X(5416) is a major center.

X(5416) lies on lines : X(6)-X(31), X(19)-X(5413) , X(40)-X(372)