X3695

X580com(EXTOUCH TRIANGLE)

X3695 = excentral-to-ABC barycentric image of X580
< 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, 37 }: Central Line L(10, 37) { 5, 312 }: Central Line L(5, 312) { 3, 345 }: Central Line L(3, 345) { 4, 346 }: Central Line L(4, 346) { 72, 306 }: Central Line L(72, 306) { 8, 405 }: Central Line L(8, 405) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_4 = ORTHOCENTER (0.6122, 0.3958) X_346 = ISOTOMIC CONJUGATE OF X(279) (0.3948, 0.0827) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_8 = NAGEL POINT (0.4694, 0.1333) X_405 = EULER LINE INTERCEPT OF LINE X(1)X(6) (0.5325, 0.1870) X_3695 = com(EXTOUCH TRIANGLE) (0.3728, 0.0510) A B C X10 X37 X5 X312 X3 X345 X4 X346 X72 X306 X8 X405 X3695 (a, b, c) = (5, 6, 7) | AB = 1

X3695 (X580com(EXTOUCH 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 \(f(a,b,c) = (b + c)^{2}(b^{2} + c ^{2} - a^{2})\)
Search Value (6, 9, 13): \(5.979350893973\)
▸ Incident Central Lines17 lines

{3, 345}, {4, 346}, {5, 312}, {8, 405}, {10, 37}, {12, 1089}, {40, 728}, {72, 306}, {78, 1062}, {100, 2915}, {190, 1330}, {304, 337}, {321, 442}, {519, 1104}, {1215, 3178}, {2049, 2345}, {3159, 3454}

▸ Functional Relations1 relation

  • X3695 = excentral-to-ABC barycentric image of X580