X3872

X2886com[INVERSE(n(4th EULER TRIANGLE))]

X3872 = {X1,X8}-harmonic conjugate of X78
< 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, 8 }: Nagel Line { 1, 2 }: Nagel Line { 75, 77 }: Central Line L(75, 77) { 34, 318 }: Central Line L(34, 318) { 63, 517 }: Central Line L(63, 517) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_1 = INCENTER (0.5714, 0.2333) X_8 = NAGEL POINT (0.4694, 0.1333) X_2 = CENTROID (0.5374, 0.2000) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_318 = ISOTOMIC CONJUGATE OF X(77) (0.5514, 0.2839) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_3872 = com[INVERSE(n(4th EULER TRIANGLE))] (0.5014, 0.1647) A B C X78 X1 X8 X2 X75 X77 X34 X318 X63 X517 X3872 (a, b, c) = (5, 6, 7) | AB = 1

X3872 (X2886com[INVERSE(n(4th EULER TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(2 + \csc^{2}(A/2) : :\) (Peter Moses, 1/13/2012)
Barycentrics: \(a(b + c - a)(b^{2} + c^{2} - a^{2} - 4bc) : :\)
Search Value (6, 9, 13): \(3.984578760112\)
▸ Incident Central Lines38 lines

{1, 2}, {9, 644}, {21, 1697}, {34, 318}, {40, 2975}, {63, 517}, {72, 1482}, {75, 77}, {100, 3576}, {104, 3359}, {149, 3586}, {280, 1219}, {355, 1532}, {391, 2324}, {392, 3305}, {404, 1420}, {515, 3434}, {518, 2099}, {529, 1836}, {908, 3421}, {946, 3436}, {952, 3419}, {958, 3057}, {960, 2098}, {993, 2802}, {996, 998}, {999, 3306}, {1060, 2968}, {1100, 3713}, {1120, 2191}, {1259, 3295}, {1319, 1376}, {2082, 2329}, {2093, 3218}, {2136, 3601}, {2345, 3554}, {2550, 3476}, {3338, 3754}

▸ Functional Relations1 relation