     X(6), X(74), X(511), X(1495), X(1976), X(13414), X(13415)     See the notations and the general properties at CL030. The isogonal transform of K223 is K953 = nK0(X2, X525) = cK(#X2, X525). K223 is also the SS{a -> a^2} image of K040. (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).  