X2423

ISOGONAL CONJUGATE OF X2397

X2423 is the isogonal conjugate of X2397.
< 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) { 6, 650 }: Central Line L(6, 650) { 31, 663 }: Central Line L(31, 663) { 104, 739 }: Central Line L(104, 739) { 604, 649 }: Central Line L(604, 649) { 81, 2401 }: Central Line L(81, 2401) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2087 = PK-TRANSFORM OF X(100) (2.1429, 2.0996) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_739 = EVEN (- 1, 0) CIRCUMCIRCLE POINT (1.0101, 0.0884) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_2401 = GIBERT-SIMSON TRANSFORM OF X(104) (1.1020, 0.1000) X_2423 = ISOGONAL CONJUGATE OF X(2397) (1.0250, 0.1225) A B C X2087 X6 X650 X31 X663 X104 X739 X604 X649 X81 X2401 X2423 (a, b, c) = (5, 6, 7) | AB = 1

X2423 (ISOGONAL CONJUGATE OF X2397) 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 given just before X2394
Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
Search Value (6, 9, 13): \(-1.099197017661\)

X2423 lies on the cubic K162.

▸ Incident Central Lines5 lines

{6, 650}, {31, 663}, {81, 2401}, {104, 739}, {604, 649}

▸ Functional Relations3 relations