Point On Object

Selection prerequisites: One or more path objects.

Constructs a point on each selected path object. The point is randomly placed on the object. It can later be animated or dragged anywhere on the object, but it will not leave the path.

Path objects on which you can construct points include straight objects (segments, rays, and lines), curved objects (circles and arcs), interior objects (polygons and circle and arc interiors), point loci, and function plots. (When you use an interior as a path, the actual path is the perimeter of that interior. A point constructed on a polygon interior is free to move around the entire perimeter of the polygon.)

You can also construct a point on an object by clicking on it with the Point tool, or with any other tool that constructs points as part of its operation (such as the Compass tool, Straightedge tools, or most custom tools).