> What are you looking for in a geometry module.  Please give an example of a
> problem you wish to pose.

At the moment it is best adapted at simple euclidean geometry question
(high school geometry and stereometry + simple operations on conics):

Give me the intersection of this and that. Define this conic, rotate
it that much, give me the intersection with this circle, etc. Test
whether this point is in this triangle, test whether this line and
this figure intersect.

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