X1269

ISOTOMIC CONJUGATE OF X1126

X1269 is the isotomic conjugate of X1126.
< 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) { 10, 75 }: Central Line L(10, 75) { 7, 349 }: Central Line L(7, 349) { 79, 314 }: Central Line L(79, 314) { 86, 310 }: Central Line L(86, 310) { 141, 321 }: Central Line L(141, 321) { 69, 674 }: Central Line L(69, 674) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4762, 0.1536) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_7 = GERGONNE POINT (0.5903, 0.2769) X_349 = ISOTOMIC CONJUGATE OF X(284) (0.5089, 0.1906) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_674 = CROSSDIFFERENCE OF X(6) AND X(514) (0.2078, -0.2856) X_1269 = ISOTOMIC CONJUGATE OF X(1126) (0.4669, 0.1460) A B C X76 X310 X10 X75 X7 X349 X79 X314 X86 X141 X321 X69 X674 X1269 (a, b, c) = (5, 6, 7) | AB = 1

X1269 (ISOTOMIC CONJUGATE OF X1126) 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 X1126)
Search Value (6, 9, 13): \(4.532002368673\)
▸ Incident Central Lines9 lines

{7, 349}, {10, 75}, {69, 674}, {79, 314}, {86, 310}, {141, 321}, {903, 1240}, {1213, 1230}, {1227, 1234}

▸ Functional Relations2 relations

Notes

X1269 is the {X75,X76}-harmonic conjugate of X313.