Determine which of the following interpretations of the undefined terms models of incidence geometry are. In any case, indicate which parallel alternative is exhibited by the interpretation.

(i) Points are points on a Euclidean plane, and lines are non-degenerate 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 Euclidean points in the interior of a fixed circle, and lines are the parts of Euclidean lines that intersect the interior of the circle.

(iv) Points are points on a Euclidean hemisphere (not including those points on the great circle that defines the hemisphere), and lines are great semicircles (i.e., those points on a great circle that intersect with the hemisphere).