> No library that I know of, but drawing tangents (and therefore,
> perpendiculars) is straight-forward:
>
>    https://tex.stackexchange.com/a/108060/323
>
> Circumcircle, orthocenter, etc... are you thinking of triangles or general
> polynomails?
>

Triangles. I understand that most of it is very easy, but still a library
will help new users.
Tikz has Tikz-Euclide and Asymptote has a Geometry package. A similar
library for Metafun
will be very useful.

-- 
Respect,
Shiv Shankar Dayal