X1057

ISOGONAL CONJUGATE OF X1056

X1057 is the isogonal conjugate of X1056.
< 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) { 78, 392 }: Central Line L(78, 392) { 77, 999 }: Central Line L(77, 999) { 29, 1058 }: Central Line L(29, 1058) { 73, 1059 }: Central Line L(73, 1059) { 497, 1065 }: Central Line L(497, 1065) { 1037, 1064 }: Central Line L(1037, 1064) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1056 = POINT ALCYONE (0.5756, 0.2499) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_392 = X(1,6)∩X(10,11) (0.5265, 0.1800) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_999 = MIDPOINT OF X(1) AND X(57) (0.5926, 0.2722) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_1058 = POINT ALKALUROPS (0.5662, 0.2123) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_1059 = ISOGONAL CONJUGATE OF X(1058) (0.5764, 0.2549) X_497 = CROSSPOINT OF GERGONNE POINT AND NAGEL POINT (0.5593, 0.1851) X_1065 = ISOGONAL CONJUGATE OF X(1064) (0.5777, 0.2607) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.5823, 0.2853) X_1064 = INTERSECTION OF LINES X(1)X(4) AND X(3)X(31) (0.5648, 0.2070) X_1057 = ISOGONAL CONJUGATE OF X(1056) (0.5671, 0.2170) A B C X1056 X78 X392 X77 X999 X29 X1058 X73 X1059 X497 X1065 X1037 X1064 X1057 (a, b, c) = (5, 6, 7) | AB = 1

X1057 (ISOGONAL CONJUGATE OF X1056) 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 \(f(A,B,C) = 1/(2 + \cos B \cos C)\)
Barycentrics: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = (\sin A) f(A,B,C)\)
Search Value (6, 9, 13): \(2.053974635810\)
▸ Incident Central Lines6 lines

{29, 1058}, {73, 1059}, {77, 999}, {78, 392}, {497, 1065}, {1037, 1064}

▸ Functional Relations1 relation