X601

INTERSECTION OF LINES X3X_31 AND X55X_255

< 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) { 3, 31 }: Central Line L(3, 31) { 35, 47 }: Central Line L(35, 47) { 40, 58 }: Central Line L(40, 58) { 1, 104 }: Central Line L(1, 104) { 4, 171 }: Central Line L(4, 171) { 55, 255 }: Central Line L(55, 255) 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_31 = 2nd POWER POINT (0.6228, 0.3008) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_40 = BEVAN POINT (0.4286, -0.0292) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_1 = INCENTER (0.5714, 0.2333) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_4 = ORTHOCENTER (0.6122, 0.3958) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_601 = INTERSECTION OF LINES X(3)X(31) AND X(55)X(255) (0.5761, 0.2252) A B C X3 X31 X35 X47 X40 X58 X1 X104 X4 X171 X55 X255 X601 (a, b, c) = (5, 6, 7) | AB = 1

X601 (INTERSECTION OF LINES X3X_31 AND X55X_255) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sin^{2} A + \cos A : \sin^{2} B + \cos B : \sin^{2} C + \cos C\)
Barycentrics: \((\sin A)(\sin^{2} A + \cos A) : (\sin B)(\sin^{2} B + \cos B) : (\sin C)(\sin^{2} C + \cos C)\)
Search Value (6, 9, 13): \(2.469482727889\)
▸ Incident Central Lines16 lines

{1, 104}, {3, 31}, {4, 171}, {5, 750}, {35, 47}, {40, 58}, {41, 906}, {55, 255}, {140, 748}, {165, 580}, {201, 920}, {371, 606}, {372, 605}, {774, 1060}, {912, 976}, {999, 1106}