X3694

X579com(EXTOUCH TRIANGLE)

X3694 = excentral-to-ABC barycentric image of X579
< 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) { 9, 55 }: Central Line L(9, 55) { 71, 72 }: Central Line L(71, 72) { 78, 219 }: Central Line L(78, 219) { 281, 318 }: Central Line L(281, 318) { 306, 307 }: Central Line L(306, 307) 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_9 = MITTENPUNKT (0.5110, 0.1615) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_281 = -CROSS CONJUGATE OF X(9) (0.5796, 0.3202) X_318 = ISOTOMIC CONJUGATE OF X(77) (0.5514, 0.2839) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_307 = ISOTOMIC CONJUGATE OF X(29) (0.4659, 0.0959) X_3694 = com(EXTOUCH TRIANGLE) (0.3640, 0.0432) A B C X10 X37 X9 X55 X71 X72 X78 X219 X281 X318 X306 X307 X3694 (a, b, c) = (5, 6, 7) | AB = 1

X3694 (X579com(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 \(f(a,b,c) = a(b + c)(b + c - a)(b^{2} + c ^{2} - a^{2})\)
Search Value (6, 9, 13): \(5.538320009710\)
▸ Incident Central Lines18 lines

{1, 2336}, {8, 2335}, {9, 55}, {10, 37}, {71, 72}, {78, 219}, {281, 318}, {306, 307}, {518, 579}, {519, 1108}, {728, 2324}, {997, 2256}, {1761, 3579}, {1792, 2193}, {1793, 2327}, {2260, 3555}, {2345, 3085}, {3061, 3169}

▸ Functional Relations1 relation

  • X3694 = excentral-to-ABC barycentric image of X579