X2442

ISOGONAL CONJUGATE OF X2416

X2442 is the isogonal conjugate of X2416.
< 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) { 4, 6 }: Van Aubel Line { 112, 1301 }: Central Line L(112, 1301) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2416 = GIBERT-SIMSON TRANSFORM OF X(1294) (-3.3289, -0.0716) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_1301 = COLLINGS TRANSFORM OF X(235) (0.6568, 0.5877) X_2442 = ISOGONAL CONJUGATE OF X(2416) (0.6310, 0.5922) A B C X2416 X4 X6 X112 X1301 X2442 (a, b, c) = (5, 6, 7) | AB = 1

X2442 (ISOGONAL CONJUGATE OF X2416) 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): \(-0.087643766754\)

X2442 lies on the cubic K162.

▸ Incident Central Lines2 lines

{4, 6}, {112, 1301}

▸ Functional Relations2 relations