X3583

INTERSECTION OF LINES X1X_4 AND X11X_30

X3583 = crosspoint of X79 and X80
< 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, 4 }: Incenter–Orthocenter Line { 5, 35 }: Central Line L(5, 35) { 11, 30 }: Central Line L(11, 30) { 55, 381 }: Central Line L(55, 381) { 56, 382 }: Central Line L(56, 382) { 20, 499 }: Central Line L(20, 499) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_11 = FEUERBACH POINT (0.7347, 0.0667) 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_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_382 = REFLECTION OF CIRCUMCENTER IN ORTHOCENTER (0.7245, 0.6894) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_499 = {X(1),X(2)}-HARMONIC CONJUGATE OF X(498) (0.4458, 0.1102) X_3583 = INTERSECTION OF LINES X(1)X(4) AND X(11)X(30) (0.1361, -1.4997) A B C X79 X80 X1 X4 X5 X35 X11 X30 X55 X381 X56 X382 X20 X499 X3583 (a, b, c) = (5, 6, 7) | AB = 1

X3583 (INTERSECTION OF LINES X1X_4 AND X11X_30) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(b^{4} + c^{4} - a^{4} - 2b^{2}c^{2} + a^{2}bc)\)
Search Value (6, 9, 13): \(7.861557029150\)
▸ Linear Combinations1 combination
▸ Incident Central Lines25 lines

{1, 4}, {5, 35}, {11, 30}, {12, 546}, {20, 499}, {55, 381}, {56, 382}, {79, 942}, {80, 517}, {115, 1914}, {149, 519}, {316, 350}, {484, 516}, {495, 3058}, {1203, 1834}, {1539, 3028}, {1749, 1776}, {1770, 3336}, {1781, 1839}, {2308, 3017}, {2964, 3073}, {3065, 3218}, {3070, 3299}, {3071, 3301}, {3100, 3153}

▸ Functional Relations8 relations

  • X3583 = reflection of Xi in Xj for these (i,j): (36, 11), (484, 1737)

  • X3583 = crosspoint of X79 and X80

  • X3583 = crosssum of X35 and X36

  • X3583 = homothetic center of 2nd isogonal triangle of X1 and the reflection of the Johnson triangle in X4; see X36

  • X3583 = homothetic center of Mandart-incircle triangle and (cross-triangle of ABC and 2nd isogonal triangle of X1)

  • X3583 = homothetic center of Ehrmann vertex-triangle and intangents triangle

  • X3583 = homothetic center of Ehrmann mid-triangle and Mandart-incircle triangle

  • X3583 = {X1,X4}-harmonic conjugate of X3585