X596

ISOGONAL CONJUGATE OF X595

X596 is the isogonal conjugate of X595.
< 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, 38 }: Central Line L(10, 38) { 37, 39 }: Central Line L(37, 39) { 58, 82 }: Central Line L(58, 82) { 65, 519 }: Central Line L(65, 519) { 244, 1089 }: Central Line L(244, 1089) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_595 = 2nd HATZIPOLAKIS-YIU POINT (0.6456, 0.3307) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_1089 = TRILINEAR SQUARE OF X(10) (0.4606, 0.1381) X_596 = ISOGONAL CONJUGATE OF X(595) (0.4466, 0.1390) A B C X595 X10 X38 X37 X39 X58 X82 X65 X519 X244 X1089 X596 (a, b, c) = (5, 6, 7) | AB = 1

X596 (ISOGONAL CONJUGATE OF X595) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/[a(a^{2} + ab + ac - bc)] : 1/[b(b^{2} + bc + ba - ca)] : 1/[c(c^{2} + ca + cb - ab)]\)
Barycentrics: \(1/(a^{2} + ab + ac - bc) : 1/(b^{2} + bc + ba - ca) : 1/(c^{2} + ca + cb - ab)\)
Search Value (6, 9, 13): \(5.411635861830\)
▸ Incident Central Lines5 lines

{10, 38}, {37, 39}, {58, 82}, {65, 519}, {244, 1089}

▸ Functional Relations3 relations