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