X3072

INTERSECTION OF X1X_3 AND X4X_31

< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 4, 31 }: Central Line L(4, 31) { 5, 238 }: Central Line L(5, 238) { 181, 389 }: Central Line L(181, 389) { 58, 515 }: Central Line L(58, 515) { 10, 580 }: Central Line L(10, 580) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_389 = CENTER OF THE TAYLOR CIRCLE (0.6078, 0.2800) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_580 = ORTHOGONAL OF X(284) (0.7089, 0.4470) X_3072 = INTERSECTION OF X(1)X(3) AND X(4)X(31) (0.6203, 0.3231) A B C X1 X3 X4 X31 X5 X238 X181 X389 X58 X515 X10 X580 X3072 (a, b, c) = (5, 6, 7) | AB = 1

X3072 (INTERSECTION OF X1X_3 AND X4X_31) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sin^{2} A + \cos B \cos C : \sin^{2} B + \cos C \cos A : \sin^{2} C + \cos A \cos B\)
Barycentrics: \(\sin^{3} A + \sin A \cos B \cos C : \sin^{3} B + \sin B \cos C \cos A : \sin^{3} C + \sin C \cos A \cos B\)
Search Value (6, 9, 13): \(-0.593432843116\)
▸ Incident Central Lines25 lines

{1, 3}, {2, 602}, {4, 31}, {5, 238}, {10, 580}, {12, 2361}, {20, 601}, {47, 1478}, {58, 515}, {155, 1740}, {181, 389}, {225, 2190}, {255, 388}, {283, 1010}, {411, 1064}, {497, 1497}, {578, 1397}, {595, 946}, {912, 1046}, {944, 1468}, {947, 1412}, {990, 1158}, {1056, 1496}, {1254, 1870}, {2179, 2201}