HYACINTHOS 24029

 

[Antreas P. Hatzipolakis]:

 

I like very much the name Clark gave to triangle NaNbNc  :)

X(10111) =  HATZIPOLAKIS-MOSES NINE-POINT-CIRCLES POINT
http://faculty.evansville.edu/ ck6/encyclopedia/ETCPart6.html #X10111

to

X(10123) =  HYACINTH-TO-EXTANGENTS-TRIANGLES PARALOGIC CENTER
http://faculty.evansville.edu/ ck6/encyclopedia/ETCPart6.html #X10119

Thanks, Clark  :)

[Randy Hutson]:

Hi Antreas,

 

I haven't had time to follow this thread, so forgive me if this was already discussed.  Having constructed the Hyacinth triangle described at X(10111), I find another triangle ('2nd Hyacinth triangle'?) which may be interesting.  It is the intersections, other than X(10111), of (Na), (Nb), (Nc) defined at X(10111).  It is also the orthogonal projections of A, B, C on the respective sides of the orthic triangle.  It is perspective to ABC at X(3) and to the orthic triangle at X(185).  Also, the trilinear product of its vertices is X(185).

 

Best regards,

Randy Hutson

[Peter Moses]:

Hi Antreas,

 

Reckon the barys for the A-vertex of this 2nd Hyacinth triangle is

{-a^4 b^2+2 a^2 b^4-b^6-a^4 c^2-4 a^2 b^2 c^2+b^4 c^2+2 a^2 c^4+b^2 c^4-c^6,b^2 (-a^2+b^2-c^2) (-a^2+b^2+c^2),c^2 (-a^2-b^2+c^2) (-a^2+b^2+c^2)}.

 

Best regards,

Peter Moses.