X3684

X3509com(EXTOUCH TRIANGLE)

X3684 = excentral-to-ABC barycentric image of X3509
< 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) { 6, 43 }: Central Line L(6, 43) { 8, 41 }: Central Line L(8, 41) { 9, 55 }: Central Line L(9, 55) { 261, 284 }: Central Line L(261, 284) { 101, 519 }: Central Line L(101, 519) { 239, 385 }: Central Line L(239, 385) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_8 = NAGEL POINT (0.4694, 0.1333) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_9 = MITTENPUNKT (0.5110, 0.1615) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_261 = ISOTOMIC CONJUGATE OF X(12) (0.5072, 0.1625) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_3684 = com(EXTOUCH TRIANGLE) (-3.2296, -2.8494) A B C X6 X43 X8 X41 X9 X55 X261 X284 X101 X519 X239 X385 X3684 (a, b, c) = (5, 6, 7) | AB = 1

X3684 (X3509com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a (a^{2}-b c) \cdot (-a+b+c) : :\)
Search Value (6, 9, 13): \(13.582355002475\)
▸ Incident Central Lines30 lines

{1, 2271}, {2, 2280}, {6, 43}, {8, 41}, {9, 55}, {72, 3496}, {78, 2082}, {100, 672}, {101, 519}, {193, 1958}, {218, 3501}, {219, 3169}, {220, 3208}, {238, 1914}, {239, 385}, {242, 740}, {261, 284}, {294, 2340}, {346, 3217}, {350, 3570}, {391, 2268}, {404, 1475}, {511, 3033}, {518, 910}, {521, 650}, {940, 1449}, {1743, 3550}, {1802, 3189}, {2266, 2550}, {2269, 2287}

▸ Functional Relations1 relation

  • X3684 = excentral-to-ABC barycentric image of X3509