X2435

ISOGONAL CONJUGATE OF X2409

X2435 is the isogonal conjugate of X2409.
< 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, 520 }: Central Line L(6, 520) { 4, 525 }: Central Line L(4, 525) { 64, 512 }: Central Line L(64, 512) { 66, 523 }: Central Line L(66, 523) { 248, 684 }: Central Line L(248, 684) { 74, 1297 }: Central Line L(74, 1297) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2409 = GIBERT-SIMSON TRANSFORM OF X(112) (0.6891, 0.5969) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_520 = ISOGONAL CONJUGATE OF X(107) (-0.0490, 0.2227) X_4 = ORTHOCENTER (0.6122, 0.3958) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_248 = -LINE CONJUGATE OF X(132) (0.8229, -0.0790) X_684 = CROSSDIFFERENCE OF X(4) AND X(32) (-1.3586, -0.3494) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_1297 = COLLINGS TRANSFORM OF X(127) (0.4838, -0.4080) X_2435 = ISOGONAL CONJUGATE OF X(2409) (2.8968, 0.1781) A B C X2409 X6 X520 X4 X525 X64 X512 X66 X523 X248 X684 X74 X1297 X2435 (a, b, c) = (5, 6, 7) | AB = 1

X2435 (ISOGONAL CONJUGATE OF X2409) 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
Search Value (6, 9, 13): \(68.180121002976\)

X2435 lies on the Jerabek hyperbola, the cubic K162.

▸ Incident Central Lines8 lines

{4, 525}, {6, 520}, {64, 512}, {66, 523}, {69, 2419}, {74, 1297}, {248, 684}, {526, 1177}

▸ Functional Relations6 relations