Re: A locus problem
- jean-pierre.ehrmann wrote:
> Dear Antreas, John and other HyacinthistsABCP.
> > > Let ABC be a triangle and P a point on its circumcircle.
> > > It is well known
> > > that the four orthocenters Hi, i = 1,2,3,4, of the triangles
> > > ABP, PAC, CPB, CAB, resp.,form a quadrilateral congruent to
> If Ha is the orthocenter of PBC,... the segments AHa, BHb, CHc, PHThat's the locus Antreas asked for. The locus of the center of this
> have the same midpoint.
> Hence the congruence is the reflection w.r.t. this point and the
> locus of the the circumcenter of (Ha,Hb,Hc,H) is the circle with
> center H, radius R.
> Best regards. Jean-Pierre
reflection (as P varies on the circumcircle) is also interesting,
because it is a trivial result that the midpoint of PH lies on the
Barry Wolk <wolkb AT ccu.umanitoba.ca>