X2980

ISOGONAL CONJUGATE OF X2979

X2980 is the isogonal conjugate of X2979.
< 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) { 22, 157 }: Central Line L(22, 157) { 5, 182 }: Central Line L(5, 182) { 95, 160 }: Central Line L(95, 160) { 53, 428 }: Central Line L(53, 428) { 1485, 2353 }: Central Line L(1485, 2353) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2979 = CENTROID OF DUAL OF THE ORTHIC TRIANGLE (0.3937, -0.0373) X_22 = EXETER POINT (0.4143, -0.1221) X_157 = -OF-TANGENTIAL-TRIANGLE (0.5266, 0.3812) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (0.5172, 0.1562) X_160 = -OF-TANGENTIAL-TRIANGLE (0.4841, -0.0647) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_428 = EULER X(38)-5th-SUBSTITUTION POINT (0.6180, 0.4109) X_1485 = PERSPECTOR OF ABC AND TANGENTIAL-OF-TANGENTIAL TRIANGLE (0.7356, 0.1420) X_2353 = -ISOCONJUGATE OF X(1760) (0.5700, 0.8373) X_2980 = ISOGONAL CONJUGATE OF X(2979) (0.6001, 0.7109) A B C X2979 X22 X157 X5 X182 X95 X160 X53 X428 X1485 X2353 X2980 (a, b, c) = (5, 6, 7) | AB = 1

X2980 (ISOGONAL CONJUGATE OF X2979) 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 \(f(a,b,c) = bc/(b^{4} + c^{4} + b^{2}c^{2} - a^{2}b^{2} - a^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-5.780785797148\)
▸ Incident Central Lines5 lines

{5, 182}, {22, 157}, {53, 428}, {95, 160}, {1485, 2353}

▸ Functional Relations4 relations