X3911

X3689com(INTOUCH TRIANGLE)

X3911 = complement of X908
< 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) incircle: Incircle of △ABC { 2, 7 }: Centroid–Gergonne Line { 10, 56 }: Central Line L(10, 56) { 36, 80 }: Central Line L(36, 80) { 109, 238 }: Central Line L(109, 238) { 65, 392 }: Central Line L(65, 392) { 11, 516 }: Central Line L(11, 516) 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_2316 = -ISOCONJUGATE OF X(1319) (1.0000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_392 = X(1,6)∩X(10,11) (0.5265, 0.1800) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_3911 = com[INTOUCH TRIANGLE))] (1.2245, 1.1998) A B C X1 X2316 X2 X7 X10 X56 X36 X80 X109 X238 X65 X392 X11 X516 X3911 (a, b, c) = (5, 6, 7) | AB = 1

X3911 (X3689com(INTOUCH 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 \(f(a,b,c) = (2a - b - c)(a + b - c)(a - b + c)\)
Search Value (6, 9, 13): \(-1.032474656736\)
▸ Linear Combinations1 combination
▸ Incident Central Lines69 lines

{1, 631}, {2, 7}, {3, 950}, {8, 1420}, {10, 56}, {11, 516}, {12, 3634}, {36, 80}, {40, 3086}, {46, 499}, {65, 392}, {73, 3216}, {88, 655}, {100, 2078}, {108, 1861}, {109, 238}, {140, 942}, {165, 497}, {201, 3670}, {208, 475}, {214, 519}, {216, 1108}, {241, 514}, {244, 3011}, {319, 2985}, {333, 1412}, {376, 3586}, {388, 1698}, {405, 1466}, {468, 1876}, {484, 3582}, {496, 3579}, {498, 3338}, {517, 1387}, {518, 3035}, {551, 2099}, {580, 3075}, {602, 1771}, {603, 1724}, {604, 1150}, {673, 927}, {750, 1471}, {899, 1458}, {902, 1647}, {914, 1813}, {936, 1467}, {938, 3523}, {993, 1470}, {1016, 1429}, {1054, 1738}, {1279, 3756}, {1357, 1463}, {1371, 1659}, {1376, 1617}, {1388, 3244}, {1402, 3741}, {1436, 1751}, {1519, 2950}, {1621, 3256}, {1699, 3474}, {1768, 1776}, {1838, 1940}, {3085, 3333}, {3321, 3323}, {3339, 3485}, {3340, 3616}, {3476, 3679}, {3487, 3525}, {3488, 3524}

▸ Functional Relations8 relations