X3410

INTERSECTION OF LINES X2X_98 AND X4X_93

< 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, 93 }: Central Line L(4, 93) { 2, 98 }: Central Line L(2, 98) { 23, 343 }: Central Line L(23, 343) { 323, 427 }: Central Line L(323, 427) { 5, 1199 }: Central Line L(5, 1199) { 68, 1173 }: Central Line L(68, 1173) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_93 = ISOGONAL CONJUGATE OF X(49) (0.5299, 0.2878) X_2 = CENTROID (0.5374, 0.2000) X_98 = TARRY POINT (0.8891, -0.2281) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_343 = ISOTOMIC CONJUGATE OF X(275) (0.4345, 0.0893) X_323 = ISOTOMIC CONJUGATE OF X(94) (-0.8839, -1.3275) X_427 = COMPLEMENT OF X(22) (0.5990, 0.3610) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1199 = 3rd SARAGOSSA POINT OF X(54) (0.5984, 0.2504) X_68 = PRASOLOV POINT (-0.0535, -0.0055) X_1173 = 1st SARAGOSSA POINT OF X(54) (0.6043, 0.2952) X_3410 = INTERSECTION OF LINES X(2)X(98) AND X(4)X(93) (0.4988, 0.2469) A B C X4 X93 X2 X98 X23 X343 X323 X427 X5 X1199 X68 X1173 X3410 (a, b, c) = (5, 6, 7) | AB = 1

X3410 (INTERSECTION OF LINES X2X_98 AND X4X_93) 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 \(f(a,b,c) = bc[abc + 2(b^{3}\cos B + c^{3}\cos C - a^{3}\cos A)]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-3.318867855559\)
▸ Incident Central Lines8 lines

{2, 98}, {4, 93}, {5, 1199}, {23, 343}, {68, 1173}, {69, 1369}, {323, 427}, {1209, 1614}