X1259

ISOGONAL CONJUGATE OF X1118

X1259 is the isogonal conjugate of X1118.
< 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, 21 }: Central Line L(8, 21) { 3, 63 }: Central Line L(3, 63) { 20, 100 }: Central Line L(20, 100) { 35, 200 }: Central Line L(35, 200) { 12, 377 }: Central Line L(12, 377) { 7, 404 }: Central Line L(7, 404) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_1264 = ISOTOMIC CONJUGATE OF X(1118) (0.2370, 0.0091) X_8 = NAGEL POINT (0.4694, 0.1333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_377 = EULER LINE INTERCEPT OF LINE X(7)X(8) (0.5473, 0.2258) X_7 = GERGONNE POINT (0.5903, 0.2769) X_404 = {X(2),X(3)}-HARMONIC CONJUGATE OF X(21) (0.5538, 0.2429) X_1259 = ISOGONAL CONJUGATE OF X(1118) (0.3105, 0.0160) A B C X345 X1264 X8 X21 X3 X63 X20 X100 X35 X200 X12 X377 X7 X404 X1259 (a, b, c) = (5, 6, 7) | AB = 1

X1259 (ISOGONAL CONJUGATE OF X1118) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as in X1118)
Search Value (6, 9, 13): \(5.235020017747\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = (\cos^{2} A)/(1 - \cos A)\)

▸ Incident Central Lines13 lines

{3, 63}, {7, 404}, {8, 21}, {12, 377}, {20, 100}, {35, 200}, {219, 283}, {255, 394}, {268, 271}, {318, 1013}, {329, 411}, {355, 1012}, {651, 1035}

▸ Functional Relations6 relations