X3761

X2276com[T(bc, c²)]

X3761 = isotomic conjugate of X751
< 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) { 1, 76 }: Central Line L(1, 76) { 36, 183 }: Central Line L(36, 183) { 43, 310 }: Central Line L(43, 310) { 75, 537 }: Central Line L(75, 537) { 385, 609 }: Central Line L(385, 609) { 34, 1235 }: Central Line L(34, 1235) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_751 = ISOGONAL CONJUGATE OF X(750) (0.5754, 0.2311) X_1 = INCENTER (0.5714, 0.2333) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4762, 0.1536) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_537 = DIRECTION OF VECTOR AX + BX + CX, where X = X(38) (-0.0190, 0.3866) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_609 = INTERSECTION OF LINES X(1)X(32) AND X(6)X(36) (0.6191, 0.3028) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_1235 = ISOTOMIC CONJUGATE OF X(1176) (0.5483, 0.2901) X_3761 = com[T(bc, c2)] (0.4942, 0.1697) A B C X751 X1 X76 X36 X183 X43 X310 X75 X537 X385 X609 X34 X1235 X3761 (a, b, c) = (5, 6, 7) | AB = 1

X3761 (X2276com[T(bc, c²)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(bc(a^{2} + 2bc) : ca(b^{2} + 2ca) : ab(c^{2} + 2ab)\)
Search Value (6, 9, 13): \(3.831615469818\)
▸ Incident Central Lines18 lines

{1, 76}, {34, 1235}, {35, 1975}, {36, 183}, {43, 310}, {69, 1478}, {75, 537}, {85, 1930}, {274, 1698}, {304, 1089}, {315, 3585}, {339, 1060}, {385, 609}, {538, 2276}, {693, 1022}, {975, 1228}, {1018, 3729}, {1914, 3734}

▸ Functional Relations2 relations