X2394

GIBERT-SIMSON TRANSFORM OF X74

X2394 = X1637-cross conjugate of X523
< 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) { 74, 98 }: Central Line L(74, 98) { 2, 525 }: Central Line L(2, 525) { 4, 523 }: Central Line L(4, 523) { 671, 1494 }: Central Line L(671, 1494) { 935, 1304 }: Central Line L(935, 1304) { 2407, 2410 }: Central Line L(2407, 2410) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2420 = ISOGONAL CONJUGATE OF X(2394) (0.8593, 0.6954) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_98 = TARRY POINT (0.8891, -0.2281) X_2 = CENTROID (0.5374, 0.2000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_4 = ORTHOCENTER (0.6122, 0.3958) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_671 = TRILINEAR POLE OF LINE X(2)X(523) (0.9639, -0.0323) X_1494 = ISOTOMIC CONJUGATE OF X(30) (0.6185, -0.1856) X_935 = POINT ALCOR (0.8281, 0.4929) X_1304 = COLLINGS TRANSFORM OF X(403) (0.7822, 0.5273) X_2407 = GIBERT-SIMSON TRANSFORM OF X(110) (1.2056, 0.9180) X_2410 = GIBERT-SIMSON TRANSFORM OF X(476) (1.4235, -0.5988) X_2394 = GIBERT-SIMSON TRANSFORM OF X(74) (1.3195, 0.1255) A B C X2420 X74 X98 X2 X525 X4 X523 X671 X1494 X935 X1304 X2407 X2410 X2394 (a, b, c) = (5, 6, 7) | AB = 1

X2394 (GIBERT-SIMSON TRANSFORM OF X74) 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) is as given just before X2394
Search Value (6, 9, 13): \(-36.670016136661\)

X2394 lies on the Kiepert hyperbola, the cubic K010.

▸ Incident Central Lines6 lines

{2, 525}, {4, 523}, {74, 98}, {671, 1494}, {935, 1304}, {2407, 2410}

▸ Functional Relations10 relations