X3584

INTERSECTION OF LINES X1X_2 AND X12X_30

< 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, 2 }: Nagel Line { 12, 30 }: Central Line L(12, 30) { 55, 381 }: Central Line L(55, 381) { 36, 495 }: Central Line L(36, 495) { 11, 547 }: Central Line L(11, 547) { 226, 484 }: Central Line L(226, 484) 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_2 = CENTROID (0.5374, 0.2000) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_495 = JOHNSON MIDPOINT (0.5666, 0.2382) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_547 = MIDPOINT OF X(2) AND X(5) (0.5468, 0.2244) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_3584 = INTERSECTION OF LINES X(1)X(2) AND X(12)X(30) (0.5552, 0.2174) A B C X1 X2 X12 X30 X55 X381 X36 X495 X11 X547 X226 X484 X3584 (a, b, c) = (5, 6, 7) | AB = 1

X3584 (INTERSECTION OF LINES X1X_2 AND X12X_30) 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 \(f(a,b,c) = bc[a^{4} + b^{4} + c^{4} - a^{2}(3bc + 2b^{2} + 2c^{2}) - 2b^{2}c^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.984339126453\)
▸ Linear Combinations1 combination
▸ Incident Central Lines21 lines

{1, 2}, {5, 3058}, {11, 547}, {12, 30}, {13, 1250}, {36, 495}, {37, 1989}, {55, 381}, {79, 3579}, {226, 484}, {376, 1478}, {388, 3524}, {542, 2330}, {553, 3336}, {599, 611}, {756, 1725}, {1479, 3545}, {1656, 3303}, {1749, 3219}, {2964, 3074}, {3304, 3526}