Ababaw Tilahun (PhD)Weldegiorgis Aregawi2018-07-112023-11-042018-07-112023-11-042011-01http://etd.aau.edu.et/handle/123456789/8026Algebraic Geometry can be used to prove geometric theorems in Euclidean Plane Geometry. This can be done when the geometric theorem has the property that the hypothesis and the conclusion of the theorem can be translated into polynomial equations. Such theorems are called admissible theorems. The geometric theorems considered involve points, lines, or circles in the Euclidean Plane which have common intersection points. In this project, first we translate the hypothesis and conclusion of the theorem in to polynomial equations. Then, the method Groebner basis is used to answer the ideal membership problem of the ideal generated by the polynomials in the hypothesis and the polynomials in the conclusion. The geometric theorems considered are the Theorem of Apollonius and Pappus Theorem which demonstrate the applicability of our methodenTheorem of Apollonius and PappusTheorem which demonstrateThesis