X1231

ISOTOMIC CONJUGATE OF X1172

X1231 is the isotomic conjugate of X1172.
< 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) { 7, 8 }: Gergonne–Nagel Line { 76, 331 }: Central Line L(76, 331) { 201, 307 }: Central Line L(201, 307) { 304, 345 }: Central Line L(304, 345) { 321, 349 }: Central Line L(321, 349) { 664, 1043 }: Central Line L(664, 1043) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1172 = 1st SARAGOSSA POINT OF X(48) (0.6100, 0.3717) X_7 = GERGONNE POINT (0.5903, 0.2769) X_8 = NAGEL POINT (0.4694, 0.1333) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_331 = ISOTOMIC CONJUGATE OF X(219) (0.6062, 0.4046) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_307 = ISOTOMIC CONJUGATE OF X(29) (0.4659, 0.0959) X_304 = ISOTOMIC CONJUGATE OF X(19) (0.3683, 0.0513) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_349 = ISOTOMIC CONJUGATE OF X(284) (0.5089, 0.1906) X_664 = TRILINEAR POLE OF LINE X(2)X(7) (0.2391, 0.5142) X_1043 = CEVAPOINT OF X(1) AND X(20) (0.4149, 0.0930) X_1231 = ISOTOMIC CONJUGATE OF X(1172) (0.4217, 0.0767) A B C X1172 X7 X8 X76 X331 X201 X307 X304 X345 X321 X349 X664 X1043 X1231 (a, b, c) = (5, 6, 7) | AB = 1

X1231 (ISOTOMIC CONJUGATE OF X1172) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(a^{2}f(a,b,c)) : 1/(b^{2}f(b,c,a)) : 1/(c^{2}f(c,a,b))\), where f(a,b,c) is as in X1172
Search Value (6, 9, 13): \(8.554857060886\)
▸ Incident Central Lines6 lines

{7, 8}, {76, 331}, {201, 307}, {304, 345}, {321, 349}, {664, 1043}

▸ Functional Relations5 relations