X2063

ORION TRANSFORM OF X69

< 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, 6 }: Centroid–Symmedian Line { 64, 207 }: Central Line L(64, 207) { 264, 801 }: Central Line L(264, 801) { 378, 1092 }: Central Line L(378, 1092) { 110, 1619 }: Central Line L(110, 1619) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_207 = -CEVA CONJUGATE OF X(34) (0.5818, 0.9198) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_801 = ISOGONAL CONJUGATE OF X(800) (0.4263, 0.1232) X_378 = REFLECTION OF X(22) IN X(3) (0.5857, 0.3262) X_1092 = TRILINEAR CUBE OF X(3) (0.3503, 0.0118) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_1619 = TCC-PERSPECTOR OF X(63) (0.4315, -1.6641) X_2063 = ORION TRANSFORM OF X(69) (0.6048, 0.2724) A B C X2 X6 X64 X207 X264 X801 X378 X1092 X110 X1619 X2063 (a, b, c) = (5, 6, 7) | AB = 1

X2063 (ORION TRANSFORM OF X69) 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 given just above X2055, using X = X69
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.547268003342\)
▸ Incident Central Lines5 lines

{2, 6}, {64, 207}, {110, 1619}, {264, 801}, {378, 1092}