(Solved): Determine which of the following interpretations of the undefined terms are models of incidence geo ...

Determine which of the following interpretations of the undefined terms are models of incidence geometry. In any case, indicate which parallel alternative is exhibited by the interpretation. (i) Points are points on a Euclidean plane, and lines are nondegenerate circles in the Euclidean plane. (ii) Points are points on a Euclidean plane, and lines are all those lines on the plane that pass through a given fixed point \( P \). (iii) Points are points on a Euclidean plane, and lines are concentric circles all having the same fixed center. (iv) Points are Euclidean points in the interior of a fixed circle, and lines are the parts of Euclidean lines that intersect the interior of the circle. Incidence Axiom 1. For each two distinct points there exists a unique line on both of them. Incidence Axiom 2. For every line there exist at least two distinct points on it. Incidence Axiom 3. There exist at least three distinct points. Incidence Axiom 4. Not all points lie on the same line.