X3685

X1757com(EXTOUCH TRIANGLE)

X3685 = excentral-to-ABC barycentric image of X1757
< 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) { 1, 87 }: Central Line L(1, 87) { 21, 261 }: Central Line L(21, 261) { 55, 312 }: Central Line L(55, 312) { 238, 239 }: Central Line L(238, 239) { 190, 518 }: Central Line L(190, 518) 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_1 = INCENTER (0.5714, 0.2333) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_261 = ISOTOMIC CONJUGATE OF X(12) (0.5072, 0.1625) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_3685 = com(EXTOUCH TRIANGLE) (-0.9728, -0.8443) A B C X8 X9 X1 X87 X21 X261 X55 X312 X238 X239 X190 X518 X3685 (a, b, c) = (5, 6, 7) | AB = 1

X3685 (X1757com(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 \(f(a,b,c) = (-a + b + c)(a^{2} - bc)\)
Search Value (6, 9, 13): \(9.867746974128\)
▸ Incident Central Lines30 lines

{1, 87}, {2, 968}, {8, 9}, {20, 2128}, {21, 261}, {31, 1999}, {55, 312}, {75, 1001}, {100, 2726}, {105, 3263}, {149, 3006}, {190, 518}, {238, 239}, {242, 862}, {321, 1621}, {344, 2550}, {345, 497}, {350, 1281}, {519, 1757}, {522, 663}, {536, 1279}, {595, 2901}, {614, 3210}, {643, 2361}, {664, 1456}, {874, 1921}, {960, 1043}, {1045, 1050}, {1265, 3189}, {1266, 3616}

▸ Functional Relations1 relation

  • X3685 = excentral-to-ABC barycentric image of X1757