X2422

ISOGONAL CONJUGATE OF X2396

X2422 is the isogonal conjugate of X2396.
< 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, 523 }: Central Line L(6, 523) { 32, 512 }: Central Line L(32, 512) { 98, 729 }: Central Line L(98, 729) { 525, 1975 }: Central Line L(525, 1975) { 876, 1910 }: Central Line L(876, 1910) { 691, 2420 }: Central Line L(691, 2420) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2086 = PK-TRANSFORM OF X(99) (1.2449, 0.9603) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_98 = TARRY POINT (0.8891, -0.2281) X_729 = EVEN (- 2, 0) CIRCUMCIRCLE POINT (1.0096, 0.1290) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_1975 = CROSSSUM OF PU(39) (0.4220, 0.1682) X_876 = ISOTOMIC CONJUGATE OF X(874) (0.9873, -0.0185) X_1910 = TRILINEAR POLE OF PU(23) (0.9516, -0.2978) X_691 = TRILINEAR POLE OF LINE X(6)X(110) (1.0101, 0.0886) X_2420 = ISOGONAL CONJUGATE OF X(2394) (0.8593, 0.6954) X_2422 = ISOGONAL CONJUGATE OF X(2396) (1.0041, 0.1128) A B C X2086 X6 X523 X32 X512 X98 X729 X525 X1975 X876 X1910 X691 X2420 X2422 (a, b, c) = (5, 6, 7) | AB = 1

X2422 (ISOGONAL CONJUGATE OF X2396) 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: \(a^{2} (b^{2} - c^{2})/(b^{4} + c^{4} - a^{2} b^{2} - a^{2} c^{2}) : :\)
Search Value (6, 9, 13): \(-0.719351083127\)

X2422 lies on the cubic K162.

▸ Incident Central Lines6 lines

{6, 523}, {32, 512}, {98, 729}, {525, 1975}, {691, 2420}, {876, 1910}

▸ Functional Relations4 relations