--- In

Hyacinthos@yahoogroups.com, "jpehrmfr" <Jean-

Pierre.Ehrmann.70@n...> wrote:

>

> To be more precise, if l = (ua+vb-wc)(-ua+vb+wc)(ua-vb+wc)

> If l>0 then Q,Q' are real and distinct; thus the locus of P is the

> circle above

> If l=0 then Q=Q' and the locus of P is the line perpendicular at Q

> to the plane ABC

> If l<0, a point P such as PA:PB:PC = u:v:w cannot exist

>

I prefer to replace "cannot exist" by "does not lie in

real space"; I encountered many geometrical problems

where e.g. a locus is imaginary except one special real point.

Also, I don't shriek back from using negative or imaginary

distances inbetween if it gives a cute result :-)

THX for verifying it's a circle - where (projected back on ABC)

does its highest/lowest point lie?

Hauke