X3582

INTERSECTION OF LINES X1X_2 AND X11X_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 { 11, 30 }: Central Line L(11, 30) { 56, 381 }: Central Line L(56, 381) { 35, 496 }: Central Line L(35, 496) { 12, 547 }: Central Line L(12, 547) { 599, 613 }: Central Line L(599, 613) 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_11 = FEUERBACH POINT (0.7347, 0.0667) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_547 = MIDPOINT OF X(2) AND X(5) (0.5468, 0.2244) X_599 = ISOTOMIC CONJUGATE OF X(598) (0.4748, 0.1327) X_613 = INTERSECTION OF LINES X(1)X(6) AND X(56)X(511) (0.5474, 0.2047) X_3582 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(30) (0.9342, 0.5888) A B C X1 X2 X11 X30 X56 X381 X35 X496 X12 X547 X599 X613 X3582 (a, b, c) = (5, 6, 7) | AB = 1

X3582 (INTERSECTION OF LINES X1X_2 AND X11X_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): \(0.903661151944\)
▸ Linear Combinations1 combination
▸ Incident Central Lines22 lines

{1, 2}, {11, 30}, {12, 547}, {35, 496}, {56, 381}, {57, 1727}, {58, 3615}, {80, 1319}, {244, 1725}, {376, 1479}, {497, 3524}, {542, 1428}, {553, 1776}, {599, 613}, {946, 3336}, {1478, 3545}, {1519, 1768}, {1656, 3304}, {1749, 3218}, {1837, 3656}, {2964, 3075}, {3303, 3526}