X1438

X294-BETH CONJUGATE OF X294

X1438 = trilinear pole of PU(48) (line X31X649)
< 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) { 1, 41 }: Central Line L(1, 41) { 32, 56 }: Central Line L(32, 56) { 58, 163 }: Central Line L(58, 163) { 86, 142 }: Central Line L(86, 142) { 87, 572 }: Central Line L(87, 572) { 6, 692 }: Central Line L(6, 692) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_294 = ISOGONAL CONJUGATE OF X(241) (0.9276, -0.0575) X_1 = INCENTER (0.5714, 0.2333) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_163 = TRILINEAR PRODUCT X(6)*X(110) (0.3174, 0.5883) X_86 = CEVAPOINT OF INCENTER AND CENTROID (0.5534, 0.2171) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_572 = ORTHOGONAL OF X(58) (7.2953, -0.6907) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_1438 = -BETH CONJUGATE OF X(294) (0.9961, -0.1135) A B C X294 X1 X41 X32 X56 X58 X163 X86 X142 X87 X572 X6 X692 X1438 (a, b, c) = (5, 6, 7) | AB = 1

X1438 (X294-BETH CONJUGATE OF X294) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X294
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(4.621111457890\)
▸ Incident Central Lines11 lines

{1, 41}, {6, 692}, {32, 56}, {58, 163}, {86, 142}, {87, 572}, {106, 919}, {269, 604}, {665, 911}, {909, 1024}, {950, 1220}

▸ Functional Relations11 relations