ADGEOM 2520

Dear friends:

 

The nine-points-circle of the Lucas-central-triangle and the circumcircle of the Lucas-tangents-triangle are tangent at:

 

T = a*(SA*(SW^2-3*S^2)+S*(SB-SC)^2) : :  (trilinears)

  = On Parry circle and  Lucas circles radical circle (1^st known center on this circle)

  = On lines: (3,3124), (23,2460), (110,371), (111,6200), (493,1976), (2502,6221), (2987,5408)

  = (3.284189707514305, 4.53142920062193, -1.012258675837407)

 

Also (see the preamble before X(6395) in ETC):

The nine-points-circle of the Lucas(-1)-central-triangle and the circumcircle of the Lucas(-1)-tangents-triangle are tangent at:

 

T*= a*(SA*(SW^2-3*S^2)-S*(SB-SC)^2) : :  (trilinears)

  = On Parry circle and  Lucas(-1) circles radical circle (1^st known center on this circle)

  = On lines: (3,3124),(23,2459), (110,372), (111,6396), (494,1976), (2502,6398) ), (2987,5409)

  = (-8.770010068776479, -0.16706981835483, 7.804025157126871)

 

The midpoint of both points is the inverse of X(3124) in the circumcircle of ABC. Therefore both points are the intersections of Parry circle with the polar of X(3124) w/r to the circumcircle of ABC.

 

Regards

César Lozada