X987

ISOGONAL CONJUGATE OF X986

X987 is the isogonal conjugate of X986.
< 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) { 8, 31 }: Central Line L(8, 31) { 9, 32 }: Central Line L(9, 32) { 4, 171 }: Central Line L(4, 171) { 3, 256 }: Central Line L(3, 256) { 58, 314 }: Central Line L(58, 314) { 7, 1106 }: Central Line L(7, 1106) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_986 = INTERSECTION OF LINES X(1)X(3) AND X(8)X(38) (0.5588, 0.2101) X_8 = NAGEL POINT (0.4694, 0.1333) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_9 = MITTENPUNKT (0.5110, 0.1615) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_4 = ORTHOCENTER (0.6122, 0.3958) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_7 = GERGONNE POINT (0.5903, 0.2769) X_1106 = TRILINEAR SQUARE OF X(56) (0.6507, 0.4375) X_987 = ISOGONAL CONJUGATE OF X(986) (0.5829, 0.2572) A B C X986 X8 X31 X9 X32 X4 X171 X3 X256 X58 X314 X7 X1106 X987 (a, b, c) = (5, 6, 7) | AB = 1

X987 (ISOGONAL CONJUGATE OF X986) 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 \(f(a,b,c) = 1/[a(b^{2} + bc + c^{2}) + b^{3} + c^{3}]\)
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): \(1.302105765102\)
▸ Incident Central Lines6 lines

{3, 256}, {4, 171}, {7, 1106}, {8, 31}, {9, 32}, {58, 314}

▸ Functional Relations1 relation