You have to clear your Graphic:
Graphics.Clear();
But all drawn figures will be cleared. Simply, you will then need to redraw all figures except that circle.
Also, you can use the Invalidate method:
Control.Invalidate()
It indicates a region to be redrawn inside your Graphics. But if you have intersecting figures you will have to redraw the figures you want visible inside the region except the circle.
This can become messy, you may want to check out how to design a control graph or use any graph layout library.
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