[Seiichi Kirikami]:
Dear friends,
the following are based on generalization 1 of Gossard perspector, Wikipedia.
1. Let ABC be a triangle and l the line through X(13) and X(15) (parallel to Euler line of ABC).
D, E, F = the intersection of l and BC, CA, AB respectively.
la, lb, lc = the Euler lines of AEF, BFD, CDE respectively.
A1, B1, C1 = the intersections of lb and lc, lc and la, la and lb respectively.
AA1, BB1, CC1 concur in a point.
For (6, 9, 13) triangle, its trilinears = (1.8412871781..,1.4018656471.. ,1.8203172594.. ).
2. Let ABC be a triangle and l the line through X(14) and X(16) (parallel to Euler line of ABC).
D, E, F = the intersection of l and BC, CA, AB respectively.
la, lb, lc = the Euler lines of AEF, BFD, CDE respectively.
A1, B1, C1 = the intersections of lb and lc, lc and la, la and lb respectively.
AA1, BB1, CC1 concur in a point.
For (6, 9, 13) triangle, its trilinears = (1.2166468764..,1.9474472132.. ,1.7309024683 ).
Best regards, Seiichi Kirikami.
the following are based on generalization 1 of Gossard perspector, Wikipedia.
1. Let ABC be a triangle and l the line through X(13) and X(15) (parallel to Euler line of ABC).
D, E, F = the intersection of l and BC, CA, AB respectively.
la, lb, lc = the Euler lines of AEF, BFD, CDE respectively.
A1, B1, C1 = the intersections of lb and lc, lc and la, la and lb respectively.
AA1, BB1, CC1 concur in a point.
For (6, 9, 13) triangle, its trilinears = (1.8412871781..,1.4018656471.. ,1.8203172594.. ).
2. Let ABC be a triangle and l the line through X(14) and X(16) (parallel to Euler line of ABC).
D, E, F = the intersection of l and BC, CA, AB respectively.
la, lb, lc = the Euler lines of AEF, BFD, CDE respectively.
A1, B1, C1 = the intersections of lb and lc, lc and la, la and lb respectively.
AA1, BB1, CC1 concur in a point.
For (6, 9, 13) triangle, its trilinears = (1.2166468764..,1.9474472132.. ,1.7309024683 ).
Best regards, Seiichi Kirikami.
[César Lozada]:
1)
Q1 = X(30)X(5459) ∩ X(402)X(5972)
= ((12*R^2-SA-2*SW)*S^2+sqrt( 3)*(-SW^2-4*SB*SC+6*SA^2+5*S^ 2+4*(SW-6*SA)*R^2)*S+(6*(3*SA- 5*SW)*R^2-2*SA^2+2*SB*SC+5*SW^ 2)*SA)*(S^2-3*SB*SC) : : (barys)
= on lines: {30, 5459}, {402, 5972}
= [ 1.8412871778471780, 1.4018656469050320, 1.8203172596591210 ]
2)
Q2 = X(30)X(5460) ∩ X(402)X(5972)
= ((12*R^2-SA-2*SW)*S^2-sqrt( 3)*(-SW^2-4*SB*SC+6*SA^2+5*S^ 2+4*(SW-6*SA)*R^2)*S+(6*(3*SA- 5*SW)*R^2-2*SA^2+2*SB*SC+5*SW^ 2)*SA)*(S^2-3*SB*SC) : : (barys)
= on lines: {30, 5459}, {402, 5972}
= [ 1.2166468763591680, 1.9474472131770760, 1.7309024683114020 ]
César Lozada
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