X1075

X3-CEVA CONJUGATE OF X4

X1075 = eigencenter of cevian triangle of X3
< 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) { 4, 51 }: Central Line L(4, 51) { 155, 450 }: Central Line L(155, 450) { 216, 631 }: Central Line L(216, 631) { 243, 920 }: Central Line L(243, 920) { 648, 1092 }: Central Line L(648, 1092) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_155 = EIGENCENTER OF ORTHIC TRIANGLE (1.1658, 0.5033) X_450 = -HIRST INVERSE OF X(4) (0.8978, 1.1430) X_216 = -CEVA CONJUGATE OF X(51) (0.5201, 0.1353) X_631 = 3/5*OG (0.5224, 0.1608) X_243 = -LINE CONJUGATE OF X(73) (0.7516, 0.9505) X_920 = -CEVA CONJUGATE OF X(1) (0.8006, 0.5344) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_1092 = TRILINEAR CUBE OF X(3) (0.3503, 0.0118) X_1075 = -CEVA CONJUGATE OF X(4) (0.6630, 1.7036) A B C X3 X4 X51 X155 X450 X216 X631 X243 X920 X648 X1092 X1075 (a, b, c) = (5, 6, 7) | AB = 1

X1075 (X3-CEVA CONJUGATE OF X4) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\sec A) (\sec^{2} B + \sec^{2} C - \sec^{2} A) : :\)
Search Value (6, 9, 13): \(2.083680761561\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\cos B \cos C (\cos^{2} C \cos^{2} A + \cos^{2} A \cos^{2} B - \cos^{2} B \cos^{2} C) : :\)

X1075 lies on the McCay cubic.

▸ Incident Central Lines5 lines

{4, 51}, {155, 450}, {216, 631}, {243, 920}, {648, 1092}

▸ Functional Relations6 relations