X983

ISOGONAL CONJUGATE OF X982

X983 is the isogonal conjugate of X982.
< 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) { 7, 171 }: Central Line L(7, 171) { 1, 182 }: Central Line L(1, 182) { 8, 238 }: Central Line L(8, 238) { 55, 256 }: Central Line L(55, 256) { 21, 976 }: Central Line L(21, 976) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_982 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(38) (0.5508, 0.1955) X_7 = GERGONNE POINT (0.5903, 0.2769) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_1 = INCENTER (0.5714, 0.2333) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_8 = NAGEL POINT (0.4694, 0.1333) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_976 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(38) (0.5520, 0.2143) X_983 = ISOGONAL CONJUGATE OF X(982) (0.5890, 0.2731) A B C X982 X7 X171 X1 X182 X8 X238 X55 X256 X21 X976 X983 (a, b, c) = (5, 6, 7) | AB = 1

X983 (ISOGONAL CONJUGATE OF X982) 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 \(f(a,b,c) = 1/[b^{2} - bc + c^{2}]\)
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): \(1.104012929320\)
▸ Incident Central Lines5 lines

{1, 182}, {7, 171}, {8, 238}, {21, 976}, {55, 256}

▸ Functional Relations2 relations