X972

ISOGONAL CONJUGATE OF X971

X972 is the isogonal conjugate of X971.
< 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) { 934, 3 }: Central Line L(934, 3) { 40, 101 }: Central Line L(40, 101) { 55, 108 }: Central Line L(55, 108) { 109, 165 }: Central Line L(109, 165) { 100, 329 }: Central Line L(100, 329) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_934 = -CROSS CONJUGATE OF X(57) (0.4269, 0.6071) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_40 = BEVAN POINT (0.4286, -0.0292) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_329 = ISOTOMIC CONJUGATE OF X(189) (0.3847, -0.0222) X_972 = ISOGONAL CONJUGATE OF X(971) (0.5731, -0.4030) A B C X934 X3 X40 X101 X55 X108 X109 X165 X100 X329 X972 (a, b, c) = (5, 6, 7) | AB = 1

X972 (ISOGONAL CONJUGATE OF X971) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/[a^{4}(b + c) - 2a^{3}(b^{2} + c^{2} - bc) + 2a(b - c)^{2}(b^{2} + c^{2} + bc) - (b - c)^{2}(b + c)^{3}] : :\)
Search Value (6, 9, 13): \(13.521784372362\)

X972 lies on the circumcircle.

▸ Incident Central Lines5 lines

{3, 934}, {40, 101}, {55, 108}, {100, 329}, {109, 165}

▸ Functional Relations6 relations

  • X972 = reflection of X934 in X3

  • X972 = isogonal conjugate of X971

  • X972 = cevapoint of X32622 and X32623

  • X972 = the point of intersection, other than A, B, and C, of the circumcircle and hyperbola {A, B, C,X4,X40,X57}}

  • X972 = Cundy-Parry Phi transform of X14256

  • X972 = Cundy-Parry Psi transform of X7367