X2989

DC(X103)

X2989 = X19-isoconjugate of X916
< 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) { 27, 110 }: Central Line L(27, 110) { 273, 651 }: Central Line L(273, 651) { 2, 1331 }: Central Line L(2, 1331) { 75, 1332 }: Central Line L(75, 1332) { 7, 1813 }: Central Line L(7, 1813) { 1815, 2400 }: Central Line L(1815, 2400) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_273 = ISOGONAL CONJUGATE OF X(212) (0.6191, 0.4329) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_2 = CENTROID (0.5374, 0.2000) X_1331 = ORTHOCORRESPONDENT OF X(101) (-0.2308, 0.2512) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_1332 = ORTHOCORRESPONDENT OF X(100) (-0.2317, 0.1866) X_7 = GERGONNE POINT (0.5903, 0.2769) X_1813 = INVERSE MIMOSA TRANSFORM OF X(650) (-0.1088, 0.3999) X_1815 = INVERSE MIMOSA TRANSFORM OF X(910) (0.6272, -0.0629) X_2400 = GIBERT-SIMSON TRANSFORM OF X(103) (1.2261, 0.1171) X_2989 = DC(X(103)) (1.3264, 0.1473) A B C X27 X110 X273 X651 X2 X1331 X75 X1332 X7 X1813 X1815 X2400 X2989 (a, b, c) = (5, 6, 7) | AB = 1

X2989 (DC(X103)) 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 X2979, using U = X103
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(4.213383146531\)

X2989 lies on the MacBeath circumconic.

▸ Incident Central Lines6 lines

{2, 1331}, {7, 1813}, {27, 110}, {75, 1332}, {273, 651}, {1815, 2400}

▸ Functional Relations6 relations