Navigation:  Menus > Construct Menu > Point on Object

Selection prerequisites: One or more path objects

This Construct menu command 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), circles, arcs, interior objects (polygons, and circle and arc interiors), point loci, function plots, and parametric plots. (When you use an interior as a path, the actual path is the perimeter of that interior. A point constructed on a polygon is free to move around the entire perimeter of the polygon.)

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