X(66) = ISOGONAL CONJUGATE OF X(22)

Trilinears

\(bc/(b4 + c4 - a4) : :\)

Barycentrics

\(1/(b4 + c4 - a4) : : Let P be a point on the circumcircle, and let LP be its Steiner line. The locus of the orthopole of LP, as P varies, is an ellipse with center :ref:`X(4) <X(4)>\) and perspector X(66). (Randy Hutson, March 29, 2020) In the plane of a triangle ABC, let`

Notes

Let P be a point on the circumcircle, and let LP be its Steiner line. The locus of the orthopole of LP, as P varies, is an ellipse with center X(4) and perspector X(66). (Randy Hutson, March 29, 2020)

In the plane of a triangle ABC, let A’B’C’ = anticomplementary triangle; Oa = circle with diameter BC, and define Ob and Oc cyclically; Ab = A’BC’&cap;Oa, and define Bc and Ca cyclically; Ac = B’CA’&cap;Oa, and define Ba and Cb cyclically; A&Prime;= BcBa&cap;CaCb, and define B&Prime; and C&Prime; cyclically. The triangle A&Prime;B&Prime;C&Prime; is perspective to ABC, and the perspector is X(66). (Dasari Naga Vijay Krishna, April 15, 2021)

X(66) lies on these lines: 2,206 3,141 6,427 68,511 73,976 193,895 248,571 290,317 879,924

X(66) = midpoint of X(2892) and X(3448)

X(66) = reflection of X(i) in X(j) for these (i,j): (159,141), (1177,125)

X(66) = isogonal conjugate of X(22)

X(66) = isotomic conjugate of X(315)

X(66) = complement of X(5596)

X(66) = anticomplement of X(206)

X(66) = cyclocevian conjugate of X(2998)

X(66) = cevapoint of X(125) and X(512)

X(66) = X(32)-cross conjugate of X(2)

X(66) = crosssum of X(3) and X(159)

X(66) = trilinear pole of line X(647)X(826) (radical axis of Brocard and polar circles)

X(66) = antigonal image of X(1177)

X(66) = orthocenter of X(3)X(4)X(2435)

X(66) = X(3174)-of-orthic-triangle if ABC is acute

X(66) = polar conjugate of isotomic conjugate of X(14376)

X(66) = X(63)-isoconjugate of X(8743)