X273

ISOGONAL CONJUGATE OF X212

X273 is the isogonal conjugate of X212.
< 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) { 4, 7 }: Central Line L(4, 7) { 29, 34 }: Central Line L(29, 34) { 27, 57 }: Central Line L(27, 57) { 2, 92 }: Central Line L(2, 92) { 28, 272 }: Central Line L(28, 272) { 75, 225 }: Central Line L(75, 225) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_4 = ORTHOCENTER (0.6122, 0.3958) X_7 = GERGONNE POINT (0.5903, 0.2769) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_2 = CENTROID (0.5374, 0.2000) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_272 = ISOGONAL CONJUGATE OF X(209) (-0.2458, -0.0534) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_273 = ISOGONAL CONJUGATE OF X(212) (0.6191, 0.4329) A B C X212 X4 X7 X29 X34 X27 X57 X2 X92 X28 X272 X75 X225 X273 (a, b, c) = (5, 6, 7) | AB = 1

X273 (ISOGONAL CONJUGATE OF X212) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sec A \sec^{2}(A/2) : \sec B \sec^{2}(B/2) : \sec C \sec^{2}(C/2)\)
Barycentrics: \(\tan A \sec^{2}(A/2) : \tan B \sec^{2}(B/2) : \tan C \sec^{2}(C/2)\)
Search Value (6, 9, 13): \(-0.638485277316\)
▸ Alternate Coordinates1 form

  • Trilinears: \((1- \sec A)\csc^{2} A : (1 - \sec B)\csc^{2} B : (1 - \sec C)\csc^{2} C\)

▸ Incident Central Lines14 lines

{2, 92}, {4, 7}, {19, 653}, {27, 57}, {28, 272}, {29, 34}, {53, 1086}, {75, 225}, {78, 322}, {108, 675}, {226, 469}, {269, 1111}, {317, 320}, {458, 894}

▸ Functional Relations8 relations