Here's a URL that will take you to a web site that will show you how as well as describe the process. http://civilwarfortifications.com/dictionary/geometric_drawing/013.html
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You can draw 9 diagonals inside a hexagon.
Yes.
A compass and straight edge.
Draw two diameter lines, then draw a circle inside the circle.
Yes you can. Any finite shape can be drawn inside any other finite shape.