X3965

X1400com(EXTOUCH TRIANGLE)

< 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, 37 }: Central Line L(8, 37) { 9, 55 }: Central Line L(9, 55) { 6, 78 }: Central Line L(6, 78) { 69, 241 }: Central Line L(69, 241) { 72, 573 }: Central Line L(72, 573) { 341, 346 }: Central Line L(341, 346) 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_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_9 = MITTENPUNKT (0.5110, 0.1615) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_573 = ORTHOHARMONIC OF X(58) (0.4486, 0.0172) X_341 = ISOTOMIC CONJUGATE OF X(269) (0.3509, 0.0650) X_346 = ISOTOMIC CONJUGATE OF X(279) (0.3948, 0.0827) X_3965 = com(EXTOUCH TRIANGLE) (0.4316, 0.0976) A B C X8 X37 X9 X55 X6 X78 X69 X241 X72 X573 X341 X346 X3965 (a, b, c) = (5, 6, 7) | AB = 1

X3965 (X1400com(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 \(f(a,b,c) = a(b + c - a)^{2}(b^{2} + c^{2} + ab + ac)\)
Search Value (6, 9, 13): \(4.916592512653\)
▸ Incident Central Lines17 lines

{6, 78}, {8, 37}, {9, 55}, {44, 2220}, {69, 241}, {72, 573}, {220, 3692}, {341, 346}, {391, 1212}, {518, 1400}, {872, 2340}, {960, 2269}, {1098, 1792}, {1211, 2092}, {1376, 2285}, {3057, 3169}, {3290, 3705}