X986

INTERSECTION OF LINES X1X_3 AND X8X_38

X986 = isogonal conjugate of X987
< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 8, 38 }: Central Line L(8, 38) { 10, 75 }: Central Line L(10, 75) { 43, 72 }: Central Line L(43, 72) { 4, 240 }: Central Line L(4, 240) { 194, 257 }: Central Line L(194, 257) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_987 = ISOGONAL CONJUGATE OF X(986) (0.5829, 0.2572) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_8 = NAGEL POINT (0.4694, 0.1333) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_4 = ORTHOCENTER (0.6122, 0.3958) X_240 = -LINE CONJUGATE OF X(48) (0.7457, 0.8594) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_986 = INTERSECTION OF LINES X(1)X(3) AND X(8)X(38) (0.5588, 0.2101) A B C X987 X1 X3 X8 X38 X10 X75 X43 X72 X4 X240 X194 X257 X986 (a, b, c) = (5, 6, 7) | AB = 1

X986 (INTERSECTION OF LINES X1X_3 AND X8X_38) 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 \(f(a,b,c) = a(b^{2} + bc + c^{2}) + b^{3} + c^{3}\)
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): \(2.081628731147\)
▸ Incident Central Lines14 lines

{1, 3}, {4, 240}, {6, 1046}, {8, 38}, {10, 75}, {43, 72}, {100, 976}, {194, 257}, {291, 337}, {386, 758}, {405, 846}, {474, 1054}, {774, 938}, {960, 978}

▸ Functional Relations1 relation