HYACINTHOS 21109

[Rand Hutson]:

> Questions:
>
> 1) What is the criteria for this set?
>
> 2) What is the general formula for the center of the bicevian conic C(P,Q),
> where P = p:q:r: and U=u:v:w?
>
> 3) Analogous questions for bianticevian conics?
>
> Thank you,
> Randy Hutson

Define cyclically x=qw, y=ru, z=pv, and x'=rv, y'=pw, z'=qu. Then x'y'z'=xyz, and
the center of the bi-anticevian conic is  (1/(x^2-x'^2): 1/(y^2-y'^2): 1/(z^2-z'^2) )
 
The bicevian conic is messier. The first coordinate of its center is
(y+z)(3+x/x')+(y'+z')(3+x'/x)-xyz(1/x-1/x')^2
--
Barry Wolk