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can anyone help me? one of my friends asked me that. how many diagonals are there in a 200 sided polygon.... as assumption she said tht triagles had no diagonals and rectangles had 2 diagonals...

Note by Niaz Shaad
3 years, 1 month ago

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200C2-200=19700. Total 19700 diagonals

Jaglul Hasan Joy - 3 years, 1 month ago

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but what is the reason?? what is the relattion with the assumption

Niaz Shaad - 3 years, 1 month ago

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See, If you know about the permutations and combinations. If n points are given to you, you can draw nC2 lines from them, given none of them are collinear. In a polygon, at most 2 points can be collinear. You need two pints 2 draw a line. So, indirectly we are finding the number of ways of selecting 2 points out of 200 = 200C2. Now these lines will also contain the sides of the polygon, So, to ignore them, we need to subtract the number of sides, which is equal to 200. Therefore, total number of diagonals = 200C2-200 = 19700

Abhineet Nayyar - 3 years, 1 month ago

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i asked her and she said its just n(n-3)/2....

Niaz Shaad - 3 years, 1 month ago

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@Niaz Shaad Yess...(nc2-n) on solving gives us (n(n-3)/2)

Abhineet Nayyar - 3 years, 1 month ago

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nC2- n where n is the number of sides in the polygon, would give you the number of diagonals. So 19700

Prashant Gudipudi - 3 years, 1 month ago

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