X1014

ISOGONAL CONJUGATE OF X210

X1014 is the isogonal conjugate of X210.
< 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, 21 }: Central Line L(7, 21) { 57, 77 }: Central Line L(57, 77) { 28, 279 }: Central Line L(28, 279) { 58, 269 }: Central Line L(58, 269) { 69, 404 }: Central Line L(69, 404) { 261, 552 }: Central Line L(261, 552) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_7 = GERGONNE POINT (0.5903, 0.2769) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_404 = {X(2),X(3)}-HARMONIC CONJUGATE OF X(21) (0.5538, 0.2429) X_261 = ISOTOMIC CONJUGATE OF X(12) (0.5072, 0.1625) X_552 = POINT MAIA I (0.6112, 0.3127) X_1014 = ISOGONAL CONJUGATE OF X(210) (0.6222, 0.3285) A B C X56 X57 X7 X21 X77 X28 X279 X58 X269 X69 X404 X261 X552 X1014 (a, b, c) = (5, 6, 7) | AB = 1

X1014 (ISOGONAL CONJUGATE OF X210) 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 \(f(a,b,c) = 1/[(b + c)(b + c - a)]\)
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): \(0.270129809458\)
▸ Incident Central Lines11 lines

{7, 21}, {28, 279}, {57, 77}, {58, 269}, {60, 757}, {69, 404}, {261, 552}, {272, 1088}, {274, 961}, {332, 1037}, {759, 934}

▸ Functional Relations6 relations