Let Pa, Qa be the points where the asymptotes of a rectangular circumhyperbola cut the side BC. Let P, Q be the intersections of the hyperbola with APa, AQa. The cevian triangles of P, Q have a side parallel to an asymptote. Let A'B'C' be the side triangle of the two cevian triangles. Then ABC, A'B'C' are perspective with center X.
For the Feuerbach hyperbola is X = X(650); for the Jerabek hyperbola is X = X(647); for the Kiepert hyperbola is X = X(523).