13485Re: [EMHL] Mittenpunkt And Concurrency Of Three Euler Lines
- Jul 1, 2006Dear Antreas,
Very nice idea! I try only some special case and we should do together to get some general results.
I am trying with first case: Q is fixed, and line is OH. I see the locus may be nice: one line?
The mittenpunkt may be is one very special case: Q = incenter I and the locus is only one point: mittenpunkt or some points?
These conjectures may be the good reasons for our efforts.
Bui Quang Tuan
PS: Please note that these only conjectures. I can confirm only with my first mittenpunkt message.
Antreas P. Hatzipolakis <xpolakis@...> wrote:
On 1-07-06, Quang Tuan Bui wrote (partly):
> Given triangle ABC, mittenpunkt Mp, incenter I. One line passingDear Tuan
> through Mp perpendicular to IA cuts lines AB, AC at Ab, Ac respectively.
> Similarly define Bc, Ba, Ca, Cb.
> 4. The most interesting:
> Three Euler lines of triangles MpBcCb, MpCaAc, MpAbBa are concurrent
> at one point P.
We have here two interesting locus families
Let ABC be a triangle, and Q,P two points.
The perpendicular to QA through P intersects AB,AC at Ab,Ac, resp.
Similarly Bc,Ba, and Ca,Cb.
Which is the locus 1. of P 2. of Q
such that the OH lines (Euler Lines) of PBcCb, PCaAc, PAbBa
Case 1 : Q = Fixed Point, P = Variable Point
Case 2 : Q = Variable Point, P = Fixed Point
Special Cases : P, or Q = I,O,H,G,K, etc
And of course we can ask for concurrence of other than OH lines
Do you Yahoo!?
Next-gen email? Have it all with the all-new Yahoo! Mail Beta.
[Non-text portions of this message have been removed]
- << Previous post in topic Next post in topic >>