In the three parts of Fig, eight points are equally spaced and marked on the circumference...

In the three parts of Fig, eight points are equally spaced and marked on the circumference of a given circle.

Figure

a) For parts (a) and (b) of Fig. 1 .8 we have two different (though congruent) triangles. These two triangles (distinguished by their vertices) result from two selections of size 3 from the vertices A, B, C, D, E, F, G, H. How many different (whether congruent or not) triangles can we inscribe in the circle in this way?

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b) How many different quadrilaterals can we inscribe in the circle, using the marked vertices? [One such quadrilateral appears in part (c) of Fig.]

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c) How many different polygons of three or more sides can we inscribe in the given circle by using three or more of the marked vertices?