X3927

X1com[INVERSE(n(EXTANGENTS TRIANGLE))]

X3927 = Conway-triangle-to-inner-Conway-triangle similarity image of X3
< 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, 30 }: Central Line L(8, 30) { 3, 63 }: Central Line L(3, 63) { 4, 144 }: Central Line L(4, 144) { 55, 191 }: Central Line L(55, 191) { 46, 210 }: Central Line L(46, 210) { 5, 329 }: Central Line L(5, 329) 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_30 = EULER INFINITY POINT (0.7469, 0.7481) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_4 = ORTHOCENTER (0.6122, 0.3958) X_144 = ANTICOMPLEMENT OF X(7) (0.4317, 0.0461) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_329 = ISOTOMIC CONJUGATE OF X(189) (0.3847, -0.0222) X_3927 = com[INVERSE(n(EXTANGENTS TRIANGLE))] (0.4485, 0.0787) A B C X8 X30 X3 X63 X4 X144 X55 X191 X46 X210 X5 X329 X3927 (a, b, c) = (5, 6, 7) | AB = 1

X3927 (X1com[INVERSE(n(EXTANGENTS 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 \(f(a,b,c) = a(2b + 2c + a)(b^{2} + c^{2} - a^{2})\)
Search Value (6, 9, 13): \(5.782065553450\)
▸ Incident Central Lines31 lines

{1, 3683}, {3, 63}, {4, 144}, {5, 329}, {8, 30}, {9, 942}, {10, 527}, {40, 971}, {46, 210}, {55, 191}, {69, 3695}, {200, 3579}, {201, 222}, {219, 3157}, {382, 3419}, {405, 3219}, {474, 3218}, {500, 3190}, {518, 3295}, {595, 3242}, {758, 958}, {894, 2049}, {896, 976}, {908, 1656}, {956, 1482}, {960, 999}, {984, 1046}, {986, 1757}, {1376, 3678}, {1698, 3715}, {1714, 3782}

▸ Functional Relations1 relation

  • X3927 = Conway-triangle-to-inner-Conway-triangle similarity image of X3