X3829

X3158com(3rd EULER TRIANGLE)

< 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) { 2, 11 }: Central Line L(2, 11) { 5, 519 }: Central Line L(5, 519) { 381, 529 }: Central Line L(381, 529) { 496, 551 }: Central Line L(496, 551) { 12, 3241 }: Central Line L(12, 3241) { 145, 3614 }: Central Line L(145, 3614) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_529 = DIRECTION OF VECTOR AX + BX + CX, where X = X(12) (0.8589, 0.6909) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_551 = MIDPOINT OF X(1) AND X(2) (0.5544, 0.2166) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_3241 = REFLECTION OF X(2) IN X(1) (0.6054, 0.2666) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_3614 = 1st HUTSON-FEUERBACH POINT (0.5602, 0.2447) X_3829 = com(3rd EULER TRIANGLE) (0.5189, 0.2125) A B C X2 X11 X5 X519 X381 X529 X496 X551 X12 X3241 X145 X3614 X3829 (a, b, c) = (5, 6, 7) | AB = 1

X3829 (X3158com(3rd EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 3b^{3} + 3c^{3} - 3ab^{2} - 3ac^{2} + 4abc - 3b^{2}c - 3bc^{2}\)
Search Value (6, 9, 13): \(2.612935237536\)
▸ Incident Central Lines7 lines

{2, 11}, {5, 519}, {12, 3241}, {145, 3614}, {381, 529}, {496, 551}, {1329, 3679}