X1820

ISOGONAL CONJUGATE OF MIMOSA TRANSFORM OF X264

X1820 is the isogonal conjugate of mimosa transform of X264.
< 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, 91 }: Central Line L(19, 91) { 68, 71 }: Central Line L(68, 71) { 1, 563 }: Central Line L(1, 563) { 1400, 1454 }: Central Line L(1400, 1454) { 1760, 1821 }: Central Line L(1760, 1821) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1748 = MIMOSA TRANSFORM OF X(264) (0.6706, 0.5179) X_19 = CLAWSON POINT (0.6246, 0.4244) X_91 = ISOGONAL CONJUGATE OF X(47) (-0.0865, -0.0205) X_68 = PRASOLOV POINT (-0.0535, -0.0055) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_1 = INCENTER (0.5714, 0.2333) X_563 = TRILINEAR PRODUCT X(47)*X(48) (0.8122, 0.3243) X_1400 = -BETH CONJUGATE OF X(37) (0.6246, 0.3268) X_1454 = -BETH CONJUGATE OF X(498) (0.6215, 0.3253) X_1760 = MIMOSA TRANSFORM OF X(305) (0.3719, -0.0901) X_1821 = ISOGONAL CONJUGATE OF MIMOSA TRANSFORM OF X(287) (0.8340, -0.1768) X_1820 = ISOGONAL CONJUGATE OF MIMOSA TRANSFORM OF X(264) (-0.0663, -0.0078) A B C X1748 X19 X91 X68 X71 X1 X563 X1400 X1454 X1760 X1821 X1820 (a, b, c) = (5, 6, 7) | AB = 1

X1820 (ISOGONAL CONJUGATE OF MIMOSA TRANSFORM OF X264) 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 \(f(a,b,c) = 1/[- (\cos A)/x + (\cos B)/y + (\cos C)/z]\),\(x : y : z\) = X264
Barycentrics: \((\sec A)/(\sec^{2} A - \csc^{2} A) : :\)
Search Value (6, 9, 13): \(0.867774020973\)
▸ Alternate Coordinates3 forms

  • Trilinears: \(\tan 2A : \tan 2B : \tan 2C\)

  • Trilinears: \(\tan A' : :\), where HaHbHc is the orthic triangle

  • Trilinears: \((1 + \cos A)/(1 + 2 \cos A) : :\)

▸ Incident Central Lines5 lines

{1, 563}, {19, 91}, {68, 71}, {1400, 1454}, {1760, 1821}

▸ Functional Relations6 relations