What is the simplest, most straightforward package for draw simple geometrical 2D sketches that involve circles, straight lines and vectors, for a professional mathematical Tex-made document? I am using Microsoft Windows.
The following sketch was made in Microsoft Word, but I need to make it more precise (ie. make right angles actually look like right angles, circles perfectly circular, and so on).
Thanks!

Some suggestions:
I have used Adobe Illustrator for publication quality diagrams like this. The free alternative to it is Inkscape. When I needed nice formulas pasted in there, I simply exported eps or png from a latex editor (e.g. this one) and placed them in the figure.
I also strongly recommend TikZ, since you don't have to export, re-embed into other programs, etc... And check out these examples! Plus TikZ is fun and pleasant to use.
Not for the faint-hearted, but you could use something like Cairo. Or just go the whole way and use OpenGL but that's probably overkill.