2012/2/1 Alexey Zaslavsky <zasl@...> ... ... and which is the locus of the point of concurrence, as P moves on the Euler line? APH [Non-text portions...
20783
Alexey Zaslavsky
zasl@...
Feb 1, 2012 1:09 pm
... ... and which is the locus of the point of concurrence, as P moves on the Euler line? The quartic, see the message of Nikos. Using the inversion with...
http://anthrakitis.blogspot.com/2012/02/six-circles.html <http://anthrakitis.blogspot.com/2012/02/six-circles.html> APH [Non-text portions of this message have...
Cosmin Pohoata and Vladimir Zajic: On a Mixtilinear Coaxality Abstract It is known that the three Apollonius circles, each passing through a vertex and its...
Dear geometers: Please, Could someone check and confirm this? Let AH, BH and CH be the orthic triangle of ABC with orthocenter H. Let A1 be the point where AAH...
You can find more points if you take the excentral triangle IaIbIc instead of your ABC and ABC instead of your orthic. APH ... [Non-text portions of this...
Thanks, Francisco. Are my calculations wrong? Regards. _____ De: Hyacinthos@yahoogroups.com [mailto:Hyacinthos@yahoogroups.com] En nombre de Francisco Javier ...
1. Let ABC be a triangle, P a point, and Pa,Pb,Pc the orth. projections of P on the altitudes ha,hb,hc resp. Which is the locus of the circumcenter of the...
1. Locus is the NPC 2. Locus is the circumcircle If, for 1., orthocenter is substituted for circumcenter, the locus is an ellipse centered at X(185), and major...
This gives another ellipse, centered at non-ETC (search 6.133993655805222), and axes parallel to the other 2. Randy ... [Non-text portions of this message have...
And for incenter, the locus is an ellipse centered at non-ETC (search 4.213190273696852) and major axis meeting line at infinity at X(3308). For symmedian...
20797
Alexey Zaslavsky
zasl@...
Feb 7, 2012 6:08 am
Dear colleagues! You can order paper version of the jcg on amazon. http://www.amazon.com/gp/product/1469941058/ Also please don't forget to send us your new...
It seems that for any point Q = (x:y:z) with respect PaPbPc, the locus of Q is a conic (an ellipse / circle) as P moves on the circumcircle. Anyway, which is...
... How about a synthetic proof that, if P lies on the circumcircle of ABC, then the circumcenter of PaPbPc lies on the NPC of ABC? APH Which is the locus of...
Another interesting result: for X(i), i=2,4,5 (and presumably any others on Euler line), the corresponding vertices of the locus ellipses are collinear, with...
... and who knows if we have similar interesting results if we take Pa,Pb, Pc as orth. projections on cevians of point P other than H! Thanks APH ... ...
In the case of the altitudes, ie cevian / pedal triangle of H, the perpendiculars from a point P to cevians AH,BH,Ch are also parallels to sidelines of ABC. ...
Dear Hyacinthists, From the first 2 definitions of Antigonal at http://bernard.gibert.pagesperso-orange.fr/gloss/pointsandmapping.html, an analog using...
http://anthrakitis.blogspot.com/2012/02/perspective.html <http://anthrakitis.blogspot.com/2012/02/perspective.html> APH [Non-text portions of this message have...
The choice of A1 and A2, etc. appears to depend on the shape of ABC. For example, for the ETC ref. triangle, it is A1B1C2 that is perspective to ABC at...
Yes, so, here is more precise information: The line A"H intersect the circumcircle at point A1, A2 with coordinates A1: {a^2 (a^2+b^2-c^2) (a^2-b^2+c^2)...
Generalization: Is it true if we replace O with a point P? (The perspector on the HP line) APH ... [Non-text portions of this message have been removed]...
Yes, it is true even if you replace O by P, It follows from the following problem:- It follows from the following problem which is a generalisation of a ...
.... and the most natural question in the world is what properties the A2,B2,C2 have?? Do we have a Picasso-like circle, which, If true (as I think), I will ...
