X947

ISOGONAL CONJUGATE OF X946

X947 is the isogonal conjugate of X946.
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 40, 77 }: Central Line L(40, 77) { 73, 102 }: Central Line L(73, 102) { 48, 282 }: Central Line L(48, 282) { 29, 515 }: Central Line L(29, 515) { 219, 572 }: Central Line L(219, 572) { 581, 1036 }: Central Line L(581, 1036) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_40 = BEVAN POINT (0.4286, -0.0292) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_282 = -CROSS CONJUGATE OF X(9) (0.6199, 0.7507) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_572 = ORTHOGONAL OF X(58) (7.2953, -0.6907) X_581 = ORTHOHARMONIC OF X(284) (0.5657, 0.2106) X_1036 = ISOGONAL CONJUGATE OF X(388) (0.5632, 0.2044) X_947 = ISOGONAL CONJUGATE OF X(946) (0.5457, 0.1609) A B C X48 X55 X40 X77 X73 X102 X282 X29 X515 X219 X572 X581 X1036 X947 (a, b, c) = (5, 6, 7) | AB = 1

X947 (ISOGONAL CONJUGATE OF X946) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a/[a^{3}(b + c) + (b - c)^{2}(a^{2} - ab - ac - b^{2} - c^{2} - 2bc)]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(5.113096212183\)
▸ Incident Central Lines8 lines

{29, 515}, {40, 77}, {48, 282}, {73, 102}, {219, 572}, {581, 1036}, {950, 1067}, {951, 1066}

▸ Functional Relations3 relations