X1738

MIMOSA TRANSFORM OF X105

X1738 = crosspoint of X75 and X673
< 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) { 19, 46 }: Central Line L(19, 46) { 10, 75 }: Central Line L(10, 75) { 1, 142 }: Central Line L(1, 142) { 43, 226 }: Central Line L(43, 226) { 238, 516 }: Central Line L(238, 516) { 240, 522 }: Central Line L(240, 522) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_673 = TRILINEAR POLE OF LINE X(1)X(514) (0.9471, -0.0769) X_19 = CLAWSON POINT (0.6246, 0.4244) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_1 = INCENTER (0.5714, 0.2333) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_1738 = MIMOSA TRANSFORM OF X(105) (-0.8367, -1.7996) A B C X75 X673 X19 X46 X10 X1 X142 X43 X226 X238 X516 X240 X522 X1738 (a, b, c) = (5, 6, 7) | AB = 1

X1738 (MIMOSA TRANSFORM OF X105) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X105
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.989820298331\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = 2abc - (b + c)[a^{2} - (b - c)^{2}]\)

▸ Incident Central Lines17 lines

{1, 142}, {2, 968}, {4, 1716}, {10, 75}, {19, 46}, {43, 226}, {225, 1788}, {238, 516}, {240, 522}, {518, 1086}, {527, 1757}, {528, 1279}, {899, 908}, {946, 978}, {1054, 1758}, {1708, 1711}, {1724, 1770}

▸ Functional Relations2 relations