Intersect Tool
Intersection points of two objects can be created in two ways:

Selecting two objects creates all intersection points (if possible).

Directly clicking on an intersection of the two objects creates only this single intersection point.
Sometimes it’s useful to display only the portions of the intersecating objects near the intersection point. To do so, open the Properties Dialog of the intersection point, and check the option Show trimmed intersection lines in the Basic tab of the Properties dialog of the object, then hide the intersecting objects. 
Outlying Intersections
For segments, rays, or arcs you may specify whether you want to Allow outlying intersections on tab Basic of the Properties Dialog. This can be used to get intersection points that lie on the extension of an object. For example, the extension of a segment or a ray is a straight line, and the extension of an arc is a circle.
See also Intersect command. 