X1435

X278-BETH CONJUGATE OF X278

X1435 = polar conjugate of X341
< 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) { 25, 34 }: Central Line L(25, 34) { 19, 57 }: Central Line L(19, 57) { 48, 223 }: Central Line L(48, 223) { 33, 354 }: Central Line L(33, 354) { 1, 951 }: Central Line L(1, 951) { 27, 1088 }: Central Line L(27, 1088) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_19 = CLAWSON POINT (0.6246, 0.4244) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_223 = -CEVA CONJUGATE OF X(57) (0.4996, -0.0528) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_354 = WEILL POINT (0.5823, 0.2533) X_1 = INCENTER (0.5714, 0.2333) X_951 = ISOGONAL CONJUGATE OF X(950) (0.5800, 0.2727) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_1088 = TRILINEAR SQUARE OF X(7) (0.6052, 0.3210) X_1435 = -BETH CONJUGATE OF X(278) (0.6337, 0.5189) A B C X278 X25 X34 X19 X57 X48 X223 X33 X354 X1 X951 X27 X1088 X1435 (a, b, c) = (5, 6, 7) | AB = 1

X1435 (X278-BETH CONJUGATE OF X278) 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 \(u : v : w\) = X278
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.014009861472\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = \tan A \tan^{2}(A/2)\)

▸ Incident Central Lines13 lines

{1, 951}, {19, 57}, {25, 34}, {27, 1088}, {33, 354}, {48, 223}, {108, 1477}, {154, 1456}, {244, 1096}, {269, 1396}, {608, 1407}, {913, 1461}, {1395, 1416}

▸ Functional Relations5 relations