X91

ISOGONAL CONJUGATE OF X47

X91 is the isogonal conjugate of X47.
< 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) { 65, 68 }: Central Line L(65, 68) { 47, 92 }: Central Line L(47, 92) { 37, 498 }: Central Line L(37, 498) { 19, 920 }: Central Line L(19, 920) { 63, 921 }: Central Line L(63, 921) { 225, 847 }: Central Line L(225, 847) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_68 = PRASOLOV POINT (-0.0535, -0.0055) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_498 = YFF CONCURRENT CONGRUENT CIRCLES POINT (0.5518, 0.2140) X_19 = CLAWSON POINT (0.6246, 0.4244) X_920 = -CEVA CONJUGATE OF X(1) (0.8006, 0.5344) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_921 = ISOGONAL CONJUGATE OF X(920) (7.0160, 1.3242) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_847 = -CROSS CONJUGATE OF X(4) (-0.1806, -0.0821) X_91 = ISOGONAL CONJUGATE OF X(47) (-0.0865, -0.0205) A B C X48 X92 X65 X68 X47 X37 X498 X19 X920 X63 X921 X225 X847 X91 (a, b, c) = (5, 6, 7) | AB = 1

X91 (ISOGONAL CONJUGATE OF X47) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sec 2A : \sec 2B : \sec 2C\)
Barycentrics: \(\sin A \sec 2A : \sin B \sec 2B : \sin C \sec 2C\)
Search Value (6, 9, 13): \(3.738569256341\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\cot A \tan 2A : :\)

▸ Incident Central Lines9 lines

{19, 920}, {31, 1087}, {37, 498}, {47, 92}, {63, 921}, {65, 68}, {225, 847}, {255, 1109}, {759, 925}

▸ Functional Relations8 relations