X3710

X1724com(EXTOUCH TRIANGLE)

X3710 = excentral-to-ABC barycentric image of X1724
< 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, 9 }: Central Line L(8, 9) { 10, 321 }: Central Line L(10, 321) { 72, 306 }: Central Line L(72, 306) { 78, 345 }: Central Line L(78, 345) { 201, 307 }: Central Line L(201, 307) { 318, 341 }: Central Line L(318, 341) 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_9 = MITTENPUNKT (0.5110, 0.1615) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_307 = ISOTOMIC CONJUGATE OF X(29) (0.4659, 0.0959) X_318 = ISOTOMIC CONJUGATE OF X(77) (0.5514, 0.2839) X_341 = ISOTOMIC CONJUGATE OF X(269) (0.3509, 0.0650) X_3710 = com(EXTOUCH TRIANGLE) (0.3219, 0.0333) A B C X8 X9 X10 X321 X72 X306 X78 X345 X201 X307 X318 X341 X3710 (a, b, c) = (5, 6, 7) | AB = 1

X3710 (X1724com(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 \(f(a,b,c) = (b + c)(b + c - a)(b^{2} + c^{2} - a^{2})\)
Search Value (6, 9, 13): \(6.105080523609\)
▸ Incident Central Lines12 lines

{8, 9}, {10, 321}, {71, 3610}, {72, 306}, {78, 345}, {145, 1453}, {201, 307}, {318, 341}, {519, 1724}, {946, 3006}, {1792, 1793}, {1834, 3175}

▸ Functional Relations1 relation

  • X3710 = excentral-to-ABC barycentric image of X1724