X3148

X262-CEVA CONJUGATE OF X6

X3148 = inverse-in-orthocentroidal circle of X2450
< 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 { 32, 51 }: Central Line L(32, 51) { 6, 157 }: Central Line L(6, 157) { 39, 184 }: Central Line L(39, 184) { 206, 570 }: Central Line L(206, 570) { 574, 1495 }: Central Line L(574, 1495) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_262 = ISOGONAL CONJUGATE OF X(182) (0.5893, 0.2856) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_157 = -OF-TANGENTIAL-TRIANGLE (0.5266, 0.3812) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_206 = -CEVA CONJUGATE OF X(32) (0.5105, -0.2297) X_570 = ORTHOGONAL OF X(52) (0.5652, 0.2098) X_574 = HARMONIC OF X(187) (0.5539, 0.1910) X_1495 = CROSSSUM OF X(2) AND X(30) (0.8194, 1.4855) X_3148 = -CEVA CONJUGATE OF X(6) (0.5769, 0.3032) A B C X262 X6 X2 X3 X32 X51 X157 X39 X184 X206 X570 X574 X1495 X3148 (a, b, c) = (5, 6, 7) | AB = 1

X3148 (X262-CEVA CONJUGATE OF X6) 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 \(x : y : z\) = X262 and \(u : v : w\) = X6
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): \(0.020043022742\)
▸ Incident Central Lines10 lines

{2, 3}, {6, 157}, {32, 51}, {39, 184}, {206, 570}, {216, 1974}, {574, 1495}, {577, 1843}, {878, 1640}, {1993, 2001}

▸ Functional Relations3 relations

Notes

As a point on the Euler line, X3148 has Shinagawa coefficients \(((E + F )F - S^{2}, -(E + F)^{2} + S^{2})\).

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