So any help would be really appreciated! I really have no idea where to start, and I can use any help.(adsbygoogle = window.adsbygoogle || []).push({});

So essentially the problem is we have a regular polygon P inscribed in a unit circle. This regular polygon has n vertices. Fix one vertex and take the product of the lengths of diagonals drawn from the one vertex to each of the other vertices.

Show that the product of these diagonals is equal to n.

...so I guess what I have so far (which is quite minimal) is this:

So I suppose I figure as much that the vertices of the regular polygon are nth roots of unity. And so I also suppose that one vertex is always 1. (1 to the nth power is always 1)

So let's label the vertices of the polygon v0, v1, v2, ... v(n-1), where v0=1.

So essentially we want to find the product |v1-1||v2-1|...|v(n-1)-1| -- and we want to show that equals n.

I guess this is what I have so far, but I'm not really sure where to go from there.

Again, any help will be greatly appreciated!

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# Product of Diagonals of Regular Polygon?

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