X3760

X2275com[T(-bc, c²)]

X3760 = isotomic conjugate of X749
< 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) { 35, 183 }: Central Line L(35, 183) { 384, 609 }: Central Line L(384, 609) { 75, 1089 }: Central Line L(75, 1089) { 33, 1235 }: Central Line L(33, 1235) { 339, 1062 }: Central Line L(339, 1062) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_749 = ISOGONAL CONJUGATE OF X(748) (0.6307, 0.4253) X_1 = INCENTER (0.5714, 0.2333) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5532, 0.2412) X_609 = INTERSECTION OF LINES X(1)X(32) AND X(6)X(36) (0.6191, 0.3028) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_1089 = TRILINEAR SQUARE OF X(10) (0.4606, 0.1381) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_1235 = ISOTOMIC CONJUGATE OF X(1176) (0.5483, 0.2901) X_339 = ISOTOMIC CONJUGATE OF X(250) (0.6002, 0.0170) X_1062 = INTERSECTION OF LINES X(1)X(3) AND X(5)X(33) (0.4633, 0.0347) X_3760 = com[T(-bc, c2)] (0.3482, 0.0495) A B C X749 X1 X76 X35 X183 X384 X609 X75 X1089 X33 X1235 X339 X1062 X3760 (a, b, c) = (5, 6, 7) | AB = 1

X3760 (X2275com[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): \(7.104263756332\)
▸ Incident Central Lines16 lines

{1, 76}, {33, 1235}, {35, 183}, {36, 1975}, {69, 1479}, {75, 1089}, {172, 3734}, {274, 3624}, {304, 1111}, {312, 1930}, {313, 3293}, {315, 3583}, {339, 1062}, {384, 609}, {538, 2275}, {668, 3632}

▸ Functional Relations2 relations