X1463

X726-BETH CONJUGATE OF X726

X1463 = X1447-Ceva conjugate of X241
< 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) { 7, 8 }: Gergonne–Nagel Line { 56, 87 }: Central Line L(56, 87) { 44, 583 }: Central Line L(44, 583) { 181, 553 }: Central Line L(181, 553) { 513, 663 }: Central Line L(513, 663) { 226, 1401 }: Central Line L(226, 1401) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_726 = EVEN (- 2, -1) INFINITY POINT (1.0187, 0.5358) X_7 = GERGONNE POINT (0.5903, 0.2769) X_8 = NAGEL POINT (0.4694, 0.1333) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_583 = ORTHOGONAL OF X(500) (0.6638, 0.3726) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_553 = POINT MAIA II (0.5963, 0.2857) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_1401 = -BETH CONJUGATE OF X(38) (0.6188, 0.3077) X_1463 = -BETH CONJUGATE OF X(726) (1.0830, 0.8620) A B C X726 X7 X8 X56 X87 X44 X583 X181 X553 X513 X663 X226 X1401 X1463 (a, b, c) = (5, 6, 7) | AB = 1

X1463 (X726-BETH CONJUGATE OF X726) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X726
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.698926364502\)
▸ Incident Central Lines7 lines

{7, 8}, {44, 583}, {56, 87}, {181, 553}, {226, 1401}, {513, 663}, {651, 1428}

▸ Functional Relations3 relations