X3136

X101-CEVA CONJUGATE OF X523

X3136 = inverse-in-orthocentroidal circle of X1011
< 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) { 2, 3 }: Euler Line { 12, 42 }: Central Line L(12, 42) { 118, 125 }: Central Line L(118, 125) { 310, 325 }: Central Line L(310, 325) { 71, 1213 }: Central Line L(71, 1213) { 672, 1901 }: Central Line L(672, 1901) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_118 = MIDPOINT OF X(4) AND X(101) (0.4133, 0.4603) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4762, 0.1536) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_1213 = ISOGONAL CONJUGATE OF X(1171) (0.5294, 0.1914) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_1901 = ZOSMA TRANSFORM OF X(1172) (0.6043, 0.3127) X_3136 = -CEVA CONJUGATE OF X(523) (0.5512, 0.2360) A B C X101 X523 X2 X3 X12 X42 X118 X125 X310 X325 X71 X1213 X672 X1901 X3136 (a, b, c) = (5, 6, 7) | AB = 1

X3136 (X101-CEVA CONJUGATE OF X523) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X101 and \(u : v : w\) = X523
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(1.380465186151\)
▸ Linear Combinations1 combination

  • X3136 = \(3a^{2}b^{2}c^{2}\) X2 + \(4S^{2}(bc + ca + ab)\) X5

▸ Incident Central Lines11 lines

{2, 3}, {12, 42}, {71, 1213}, {118, 125}, {310, 325}, {672, 1901}, {1211, 2886}, {1214, 1893}, {1230, 3006}, {1836, 2245}, {2238, 2911}

▸ Functional Relations5 relations

Notes

As a point on the Euler line, X3136 has Shinagawa coefficients \((\$aS_{A}S_{B}\$-\$aS_{C}S_{A}\$ +\$aS_{C}\$F-\$aS_{B}\$F, \$aS_{C}^{2}\$ -\$aS_{B}^{2}\$)\).