X3871

X12com[INVERSE(n(4th EULER TRIANGLE))]

X3871 = intouch-to-ABC barycentric image of X12
< 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) { 8, 21 }: Central Line L(8, 21) { 1, 88 }: Central Line L(1, 88) { 3, 145 }: Central Line L(3, 145) { 5, 149 }: Central Line L(5, 149) { 2, 496 }: Central Line L(2, 496) { 12, 528 }: Central Line L(12, 528) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1 = INCENTER (0.5714, 0.2333) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_149 = REFLECTION OF X(20) IN X(104) (1.3265, -0.3333) X_2 = CENTROID (0.5374, 0.2000) 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_528 = DIRECTION OF VECTOR AX + BX + CX, where X = X(11) (1.0237, -0.1286) X_3871 = com[INVERSE(n(4th EULER TRIANGLE))] (0.5906, 0.2228) A B C X8 X21 X1 X88 X3 X145 X5 X149 X2 X496 X12 X528 X3871 (a, b, c) = (5, 6, 7) | AB = 1

X3871 (X12com[INVERSE(n(4th 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 \(f(a,b,c) = a(b + c - a)(a^{2} + ab + ac - bc)\)
Search Value (6, 9, 13): \(1.349600532013\)
▸ Incident Central Lines41 lines

{1, 88}, {2, 496}, {3, 145}, {5, 149}, {8, 21}, {10, 1621}, {12, 528}, {35, 519}, {36, 3244}, {41, 644}, {56, 3241}, {60, 643}, {72, 1005}, {78, 1697}, {238, 3214}, {380, 3692}, {390, 2478}, {405, 3617}, {411, 517}, {452, 1260}, {474, 3622}, {495, 2475}, {595, 3293}, {943, 3419}, {956, 3621}, {960, 3689}, {993, 3632}, {999, 3623}, {1036, 1261}, {1329, 3058}, {1334, 3684}, {1376, 3303}, {1468, 3550}, {1470, 1476}, {2136, 3601}, {2268, 3169}, {2280, 3501}, {2346, 2550}, {2476, 3085}, {3218, 3555}, {3685, 3701}

▸ Functional Relations1 relation

  • X3871 = intouch-to-ABC barycentric image of X12