X2053

X2-ISOCONJUGATE OF X1423

X2053 = X9-cross conjugate of X55
< 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) { 56, 87 }: Central Line L(56, 87) { 31, 172 }: Central Line L(31, 172) { 105, 330 }: Central Line L(105, 330) { 6, 904 }: Central Line L(6, 904) { 1403, 1580 }: Central Line L(1403, 1580) { 3, 2108 }: Central Line L(3, 2108) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_330 = ISOTOMIC CONJUGATE OF X(192) (0.4364, 0.1391) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_904 = -HIRST INVERSE OF X(256) (0.6163, 0.2816) X_1403 = -BETH CONJUGATE OF X(43) (0.6606, 0.3972) X_1580 = POINT ALUDRA (1.3094, 1.2033) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2108 = POINT KEPLER I (-0.3883, 0.6500) X_2053 = -ISOCONJUGATE OF X(1423) (0.4486, 0.1337) A B C X56 X87 X31 X172 X105 X330 X6 X904 X1403 X1580 X3 X2108 X2053 (a, b, c) = (5, 6, 7) | AB = 1

X2053 (X2-ISOCONJUGATE OF X1423) 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 \(f(a,b,c) = a(b + c - a)/(ab + ac - bc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(6.118412760565\)
▸ Incident Central Lines9 lines

{3, 2108}, {6, 904}, {31, 172}, {41, 2330}, {55, 2319}, {56, 87}, {105, 330}, {1403, 1580}, {2115, 2144}

▸ Functional Relations5 relations