9625Re: Two equivalent theorems (an old and a new(?))
- Apr 1, 2004--- In Hyacinthos@yahoogroups.com, "Antreas P. Hatzipolakis"
> Let ABC be a triangle, H its orthocenter and P a point.HP.
> OLD THEOREM:
> The reflections of the line HP in the sidelines of ABC concur
> at P' on the circumcircle of ABC.
> NEW(?) THEOREM:
> Let A', B', C' be the orthogonal projections of A,B,C on the line
> The reflections of AA', BB', CC' in the angle bisectors AA*, BB*,CC* (resp.)
> of ABC concur at P' on the circumcircle of ABC.I'm sure the fact that the Simson line of P' is parallel to HP helps,
but it's 4 AM here (in Romania), so I'm going to think it through
tomorrow morning :).
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