X967

ISOGONAL CONJUGATE OF X966

X967 is the isogonal conjugate of X966.
< 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) { 3, 42 }: Central Line L(3, 42) { 25, 58 }: Central Line L(25, 58) { 37, 63 }: Central Line L(37, 63) { 27, 393 }: Central Line L(27, 393) { 81, 941 }: Central Line L(81, 941) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_966 = INTERSECTION OF LINES X(2)X(6) AND X(4)X(9) (0.5191, 0.1803) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_941 = ISOGONAL CONJUGATE OF X(940) (0.5671, 0.2256) X_967 = ISOGONAL CONJUGATE OF X(966) (0.6112, 0.2884) A B C X966 X3 X42 X25 X58 X37 X63 X27 X393 X81 X941 X967 (a, b, c) = (5, 6, 7) | AB = 1

X967 (ISOGONAL CONJUGATE OF X966) 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 \(f(a,b,c) = a/[a^{2} - 2a(b + c) - (b + c)^{2}]\)
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): \(0.712576833950\)
▸ Incident Central Lines5 lines

{3, 42}, {25, 58}, {27, 393}, {37, 63}, {81, 941}

▸ Functional Relations2 relations