X3482

ISOGONAL CONJUGATE OF X3481

X3482 is the isogonal conjugate of X3481.
< 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, 1157 }: Central Line L(4, 1157) { 3, 2121 }: Central Line L(3, 2121) { 30, 3481 }: Central Line L(30, 3481) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3481 = INTERSECTION OF LINES X(3)X(2120) and X(4)X(2121) (0.5519, 0.7884) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1157 = INVERSE-IN-CIRCUMCIRCLE OF X(54) (1.5871, 1.5280) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2121 = ISOGONAL CONJUGATE OF X(2120) (0.6451, 0.1816) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_3482 = ISOGONAL CONJUGATE OF X(3481) (0.2339, -0.0437) A B C X3481 X4 X1157 X3 X2121 X30 X3482 (a, b, c) = (5, 6, 7) | AB = 1

X3482 (ISOGONAL CONJUGATE OF X3481) 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 \(f(a,b,c) = 1/x(3481)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-2.791794330141\)

X3482 lies on the Neuberg cubic.

▸ Incident Central Lines3 lines

{3, 2121}, {4, 1157}, {30, 3481}

▸ Functional Relations2 relations

  • X3482 = isogonal conjugate of X3481

  • X3482 = antigonal conjugate of X34304