To construct a hexagon, draw a circle. Next, (using the same compass setting), select a random point on the circle (this will later be a vertex of the finished polygon) and draw another circle. This circle should, if drawn correctly, intersect the outside of the circle in two places and just touch the center of the first circle. In a place where the second circle crosses the first, repeat the process. Continue in this manner until you reach the beginning. Connect every point that touches the very first circle that you drew. Those line segments form a regular hexagon.

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