Point on Object Tool
From GeoGebra Manual
To create a point, which is fixed to an object, click on the tool button first and then on the object. This new point can be moved via Move Tool, but only within the object.
Note: To put a point in the interior of a Circle or Ellipse, then you will need to increase the Opacity from 0 first. If you click on the perimeter of an object (eg Circle, Ellipse, Polygon), then the point will be fixed to the perimeter rather than the interior.