TITLE: Is it possible to solve any Euclidean geometry problem using a computer?
QUESTION [29 upvotes]: By "problem", I mean a high-school type geometry problem.
If no, is there other set of axioms that allows that?
If yes, are there any software that does that?
I did a search, but was not able to find a single program that allows that. It is strange because even if it is impossible to solve any problem, most of the natural problems should be solvable.

REPLY [3 votes]: As far as I know there is no practical tool which provide automatically a readable proofs of the same kind as high school proofs for many geometry theorems.
As Mitch pointed there are algebraic methods such as Grobner bases and Wu's method, but they do not provide readable proofs. They have been implemented and are available in software such as:
opengeoprover (an open source implementation in java), Predrag Janicic's gclc, geother by Dong Ming Wang (a maple implementation of Wu's method)...
Some provers are also available in GeoGebra 5.
There is also a method which produces proofs which sometimes can be considered readable: The area method by Chou, Gao and Zhang.
This method is implemented in open-geo-prover and I have implemented it in Coq.
There is also an old paper by Gelertner which describes an approach which try to mimic the human proofs (but as far as I know this method is not very efficient):
http://aitopics.org/sites/default/files/classic/Feigenbaum_Feldman/Computers_And_Thought-Part_1_Geometry.pdf