Does Sage have, or is there a package I can add, that implements basic 
plane geometry objects and operations. The sort of thing I'd like to do is, 
given two points, construct the line that contains them. Or given two 
circles, intersect them yielding 0, 1, or 2 points. Given a set of points, 
determine which are on the convex hull, construct that polygon, and return 
its area. And, ultimately, after working with various geometric objects, 
perhaps visualize them on the screen (but that comes later). 

Extra bonus if I can do this in both the Euclidean plane and the Hyperbolic 
plane (and in the latter case visualize either in the Poincare disk or the 
upper half plane models). 

Thanks.

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