X1149

ISOGONAL CONJUGATE OF X1120

X1149 is the isogonal conjugate of X1120.
< 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) { 1, 2 }: Nagel Line { 36, 106 }: Central Line L(36, 106) { 38, 392 }: Central Line L(38, 392) { 244, 517 }: Central Line L(244, 517) { 31, 999 }: Central Line L(31, 999) { 513, 663 }: Central Line L(513, 663) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_392 = X(1,6)∩X(10,11) (0.5265, 0.1800) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_999 = MIDPOINT OF X(1) AND X(57) (0.5926, 0.2722) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_1149 = ISOGONAL CONJUGATE OF X(1120) (1.1667, 0.8165) A B C X1 X106 X2 X36 X38 X392 X244 X517 X31 X999 X513 X663 X1149 (a, b, c) = (5, 6, 7) | AB = 1

X1149 (ISOGONAL CONJUGATE OF X1120) 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 \(f(a,b,c) = a(b^{2} + c^{2} + ba + ca - 4bc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.333637906544\)
▸ Incident Central Lines8 lines

{1, 2}, {31, 999}, {36, 106}, {38, 392}, {244, 517}, {513, 663}, {672, 1015}, {748, 956}

▸ Functional Relations6 relations