X3825

X56com(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) { 10, 11 }: Central Line L(10, 11) { 2, 35 }: Central Line L(2, 35) { 5, 515 }: Central Line L(5, 515) { 12, 551 }: Central Line L(12, 551) { 56, 535 }: Central Line L(56, 535) { 496, 519 }: Central Line L(496, 519) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_2 = CENTROID (0.5374, 0.2000) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_551 = MIDPOINT OF X(1) AND X(2) (0.5544, 0.2166) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_535 = DIRECTION OF VECTOR AX + BX + CX, where X = X(36) (0.8224, 0.7130) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_3825 = com(3rd EULER TRIANGLE) (0.5373, 0.1741) A B C X10 X11 X2 X35 X5 X515 X12 X551 X56 X535 X496 X519 X3825 (a, b, c) = (5, 6, 7) | AB = 1

X3825 (X56com(3rd EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \((b-c)^{2} a^{2}-(b+c) b c a-(b^{2}-c^{2})^{2} : :\)
Search Value (6, 9, 13): \(2.938288439102\)
▸ Incident Central Lines17 lines

{2, 35}, {5, 515}, {10, 11}, {12, 551}, {37, 1506}, {56, 535}, {404, 3583}, {495, 3636}, {496, 519}, {499, 993}, {758, 1210}, {946, 3754}, {1001, 1656}, {2476, 3624}, {2886, 3634}, {2975, 3582}, {3452, 3678}