Once a circle has been drawn, there is no way to delete it. So, you need to clear the entire canvas with the background color and redraw everything.
So, you need to:
Come up with a bunch of "shape" classes for representing each line and each ark and each circle. They will probably all derive from some common base "Shape" class which offers methods that are common to all shapes, for example, a method to draw the shape on a canvas.
Instantiate objects from these classes to represent the shapes that are supposed drawn on the screen, and keep these objects in a list throughout the lifetime of your application.
When the event occurs, you make any changes to your shapes, (in your case, remove a circle and add another circle, or, more likely, change the coordinates of an existing circle without removing it and re-inserting it in the list,) and then you need to invalidate the canvas control that you presumably use for painting, (search for "Invalidate" for documentation,) so as to cause the canvas to repaint itself.
You override the paint method of the canvas control so as to do your painting: first you clear the control to its background color, and then you iterate through your list of shapes, calling each shape to draw itself on the canvas.
Of course this will cause flicker; if that's unacceptable, then you will need to read up on how to implement "double buffering" (look it up) to eliminate the flicker.
Another approach for flicker elimination is to only erase and repaint the area that has changed. In your case, that would be the smallest rectangle that contains both the circle in its old location, and the circle in its new location. So, instead of invalidating the entire canvas, you invalidate only that rectangle. The problem with this approach is that other shapes that cross the invalidated area might appear to be redrawn somewhat inaccurately. This may be unacceptable, or it may be acceptable, you will not know unless you try it.