X1257

ISOGONAL CONJUGATE OF X1104

X1257 is the isogonal conjugate of X1104.
< 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) { 28, 72 }: Central Line L(28, 72) { 57, 78 }: Central Line L(57, 78) { 8, 278 }: Central Line L(8, 278) { 69, 279 }: Central Line L(69, 279) { 105, 960 }: Central Line L(105, 960) { 200, 1254 }: Central Line L(200, 1254) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1104 = CROSSPOINT OF X(1) AND X(28) (0.6311, 0.3042) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_8 = NAGEL POINT (0.4694, 0.1333) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5041, 0.1533) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_1254 = ISOGONAL CONJUGATE OF X(1098) (0.6258, 0.3523) X_1257 = ISOGONAL CONJUGATE OF X(1104) (0.4843, 0.1638) A B C X1104 X28 X72 X57 X78 X8 X278 X69 X279 X105 X960 X200 X1254 X1257 (a, b, c) = (5, 6, 7) | AB = 1

X1257 (ISOGONAL CONJUGATE OF X1104) 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 X1104)
Search Value (6, 9, 13): \(3.782859942396\)
▸ Incident Central Lines8 lines

{2, 1265}, {8, 278}, {28, 72}, {57, 78}, {69, 279}, {105, 960}, {200, 1254}, {518, 961}

▸ Functional Relations2 relations