You can find it useful to read the section "automatic geometric theorem proving" in the book "ideals, varieties and algorithms" by Cox, Little and o'shea

Thank you Seyed.

In addition to what @Seyed Hamid Hassanzadeh has observed, you may find it useful the following excellent paper:

S.G. Krantz, The history and concept of mathematical proof, 2007:

http://www.math.wustl.edu/~sk/eolss.pdf

Computer-generated proofs are covered in Section 8, starting on page 30.    Euclid as a geometer is considered in Section 4.3, starting on page 13.

And closer to what you are looking for is

D. Wang, On Wu's method for proving constructive geometric theorems:

http://ijcai.org/Past%20Proceedings/IJCAI-89-VOL1/PDF/067.pdf

And a geometry theorem prover is introduced in

S. Stojanovic, V. Pavlovic, P. Janicic, A coherent logic based geometry theorem prover…:

http://poincare.matf.bg.ac.rs/~janicic/papers/2011-adg-argoclp.pdf

Additionally see 'Geometric Theorem Proving' of next excellent introduction to Groebner Basis:

http://www.scholarpedia.org/article/Groebner_basis