The following illustrations show a sequence of some of the possibilities resulting from inscribing diameters, arcs, and other chords. Construct point A as the center of a circle. Make point B on the circumference of a circle using a clear transparent plastic cover of any coffee can.
Note that arcs must intersect both the center of the circle and its circumference.
If you have the Geometer's Sketchpad, here's a sketch to print out (53K).

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