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).