See the notations and the general properties at CL030.
(Comments below by Wilson Stothers)
C(R) is the Jerabek Hyperbola. R* = X(112). T(R*) is the line X(6)X(25).
K223 is :
- The locus of X such that XX* has mid-point on the Brocard Axis.
- The locus of X such that XX* is divided harmonically by the Lemoine Axis (T(K)) and the tangent to C(R) at K - this is the line KX(25) and the tripolar of R*.
- The K-Hirst inverse of C(R).
K223 contains :
- K, the node,
- X(74) as the intersection of C(K) and C(R),
- X(511) as the infinite point of the Brocard axis or as the isoconjugate of O,
- X(1495) as the intersection of T(K) and T(R*),
- X(1976) as the isoconjugate of X(511).
- S1, S2 as in Table 62. K223 is actually also invariant under the JS involution described in Table 62.
The nodal tangents are
- The tangents from K to I(R*)
- The tripolars of the intersections of T(R*) and C(K)
- The lines from K to the intersections of C(R) and the Lemoine axis.
The pivotal conic touches the Lemoine axis at R. This identifies it as an inconic of the tangential triangle with center X(924).