X2408

GIBERT-SIMSON TRANSFORM OF X111

X2408 = isogonal conjugate of X2434
< 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) { 2, 523 }: Central Line L(2, 523) { 690, 895 }: Central Line L(690, 895) { 691, 2407 }: Central Line L(691, 2407) { 892, 2396 }: Central Line L(892, 2396) { 1499, 1992 }: Central Line L(1499, 1992) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2434 = ISOGONAL CONJUGATE OF X(2408) (-0.7602, -0.7083) X_2 = CENTROID (0.5374, 0.2000) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_690 = CROSSDIFFERENCE OF LINE X(6) AND X(110) (0.0840, -0.1726) X_895 = ISOGONAL CONJUGATE OF X(468) (0.9484, -0.0134) X_691 = TRILINEAR POLE OF LINE X(6)X(110) (1.0101, 0.0886) X_2407 = GIBERT-SIMSON TRANSFORM OF X(110) (1.2056, 0.9180) X_892 = ISOGONAL CONJUGATE OF X(351) (1.0590, 0.0699) X_2396 = GIBERT-SIMSON TRANSFORM OF X(99) (-8.5185, -6.6572) X_1499 = POINT BIHAM (0.1078, 0.5997) X_1992 = ORTHOCORRESPONDENT OF X(2) (0.6626, 0.3345) X_2408 = GIBERT-SIMSON TRANSFORM OF X(111) (0.9952, 0.0250) A B C X2434 X2 X523 X690 X895 X691 X2407 X892 X2396 X1499 X1992 X2408 (a, b, c) = (5, 6, 7) | AB = 1

X2408 (GIBERT-SIMSON TRANSFORM OF X111) 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 \(f(a,b,c) = bc(b^{2} - c^{2})(5a^{2} - b^{2} - c^{2})/(2a^{2} - b^{2} - c^{2})\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.340611126583\)

X2408 lies on the cubic K010.

▸ Incident Central Lines5 lines

{2, 523}, {690, 895}, {691, 2407}, {892, 2396}, {1499, 1992}

▸ Functional Relations4 relations