X913

POINT AGENA

X913 = isogonal conjugate of X914
< 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) { 19, 101 }: Central Line L(19, 101) { 27, 662 }: Central Line L(27, 662) { 25, 692 }: Central Line L(25, 692) { 571, 608 }: Central Line L(571, 608) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_914 = ISOGONAL CONJUGATE OF X(913) (-2.5447, -1.0613) X_19 = CLAWSON POINT (0.6246, 0.4244) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_662 = TRILINEAR POLE OF LINE X(1)X(21) (0.1811, 0.4951) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_692 = -CEVA CONJUGATE OF X(101) (0.2833, 0.5715) X_571 = ORTHOHARMONIC OF X(52) (0.7141, 0.4556) X_608 = ISOGONAL CONJUGATE OF X(345) (0.6361, 0.4975) X_913 = POINT AGENA (0.8959, 0.3579) A B C X914 X19 X101 X27 X662 X25 X692 X571 X608 X913 (a, b, c) = (5, 6, 7) | AB = 1

X913 (POINT AGENA) 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 \(f(a,b,c) = a/[(wb + vc)/a - v - w]\),\(u : v : w\) = X4
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(-46.970810800138\)
▸ Incident Central Lines4 lines

{19, 101}, {25, 692}, {27, 662}, {571, 608}

▸ Functional Relations1 relation