12548Re: [EMHL] Looking for an explanation
- Apr 1, 2006Dear Bernard and Steve
> >> [JP] consider the rectangular hyperbola through G, O, Kthrough
> >> (symedian), X[110).
> >> His center is the midpoint of GX and the hyperbola goes
> >> the infinite points of the Jerabek hyperbola, X, X, XI don't think so
> >> , X
> >> ,...
> >> Consider a common point P (not X) of the hyperbola with the
> >> circumcircle;
> These 3 points P lie on the Thomson cubic.
> >> let M be the homothetic of P in (O, -3) and A'B'C' theDarboux
> >> pedal triangle of M.
> >> Then AA', BB', CC' are parallel.
> >> Any explanation?
> there's a close analogy with the bottom of my web page on the
It is quite interesting to see that these points are the only points
P in the plane such as, if A'B'C' is the pedal triangle of P, the
lines AA', BB', CC' are parallel (of course they are parallel to the
asymptots of Lucas - or Thomson -)
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