X979

X8-CROSS CONJUGATE OF X1

X979 = isogonal conjugate of X978
< 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) { 10, 87 }: Central Line L(10, 87) { 43, 58 }: Central Line L(43, 58) { 56, 978 }: Central Line L(56, 978) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_1 = INCENTER (0.5714, 0.2333) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_978 = -CEVA CONJUGATE OF X(1) (0.7456, 0.4040) X_979 = -CROSS CONJUGATE OF X(1) (-0.0435, -0.0124) A B C X8 X1 X10 X87 X43 X58 X56 X978 X979 (a, b, c) = (5, 6, 7) | AB = 1

X979 (X8-CROSS CONJUGATE OF X1) 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 \(f(a,b,c) = 1/[a^{2}(b + c) + a(b^{2} - bc + c^{2}) - bc(b + c)]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(-7.385519455995\)
▸ Incident Central Lines3 lines

{10, 87}, {43, 58}, {56, 978}

▸ Functional Relations2 relations