X1002

ISOGONAL CONJUGATE OF X1001

X1002 is the isogonal conjugate of X1001.
< 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) { 42, 57 }: Central Line L(42, 57) { 6, 105 }: Central Line L(6, 105) { 55, 81 }: Central Line L(55, 81) { 2, 210 }: Central Line L(2, 210) { 8, 274 }: Central Line L(8, 274) { 65, 279 }: Central Line L(65, 279) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1001 = MIDPOINT OF X(1) AND X(9) (0.5412, 0.1974) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_2 = CENTROID (0.5374, 0.2000) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_8 = NAGEL POINT (0.4694, 0.1333) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_1002 = ISOGONAL CONJUGATE OF X(1001) (0.5967, 0.2704) A B C X1001 X42 X57 X6 X105 X55 X81 X2 X210 X8 X274 X65 X279 X1002 (a, b, c) = (5, 6, 7) | AB = 1

X1002 (ISOGONAL CONJUGATE OF X1001) 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 \(f(a,b,c) = 1/[a^{2} - a(b + c) - 2bc]\)
Search Value (6, 9, 13): \(0.944907911168\)
▸ Incident Central Lines10 lines

{1, 672}, {2, 210}, {6, 105}, {8, 274}, {28, 607}, {42, 57}, {55, 81}, {65, 279}, {145, 330}, {277, 942}

▸ Functional Relations4 relations