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How many diagonals does a polygon with 21 sides have, if one

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How many diagonals does a polygon with 21 sides have, if one [#permalink] New post 09 Feb 2006, 17:00
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. How many diagonals does a polygon with 21 sides have, if one of its vertices does not connect to any diagonal?

a) 21
b) 170
c) 340
d) 357
e) 420
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 [#permalink] New post 09 Feb 2006, 17:49
Somehow I am getting 171 :roll:

All the lines that can be drawn with 21 points = 21C2 =
Number of sides = 21

So number of diagonals when diagonals are drawn from all edges = 210 - 21 = 189 (Subtract the number of sides)

Number of missing diagonals when one of the vertex does not have any diagonals= 21-3 = 18 (By drawing some of the known polygons... you can see n-3 disgonals will be missing)

Total = 189-18 = 171

Any comments?
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 [#permalink] New post 10 Feb 2006, 00:23
21 points One does not participate...20 points.

So joining 20 points combinations are C(20,2) = 10*19 = 180

Outof this there will be 20-1=19 are valid sides of polygon so 180-19=171... :roll: :roll: :roll:
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 [#permalink] New post 10 Feb 2006, 01:06
C. 340

polygon 0f 21 sides.... one side does not connect to any diagonal..

21-1= 20, from any point there will be 17 diagonal (20-3) because the point in consideration is connected to two other point of the polygon

17*20 = 340
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 [#permalink] New post 10 Feb 2006, 08:30
SunShine wrote:
C. 340

polygon 0f 21 sides.... one side does not connect to any diagonal..

21-1= 20, from any point there will be 17 diagonal (20-3) because the point in consideration is connected to two other point of the polygon

17*20 = 340


If A connects to B and B connects back to A both are same diagonal!
so 340/2 = 170

More over you also need to consider one special case where end two points conencts to each other so its 170+1=171 !

what is OA/OE?
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 [#permalink] New post 11 Feb 2006, 03:48
giddi77 wrote:
Somehow I am getting 171 :roll:

All the lines that can be drawn with 21 points = 21C2 =
Number of sides = 21

So number of diagonals when diagonals are drawn from all edges = 210 - 21 = 189 (Subtract the number of sides)

Number of missing diagonals when one of the vertex does not have any diagonals= 21-3 = 18 (By drawing some of the known polygons... you can see n-3 disgonals will be missing)

Total = 189-18 = 171

Any comments?


Giri , i came up to the same approach till the last step where u subtracted 3 from 21 ! can u explain that for me.
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  [#permalink] 11 Feb 2006, 03:48
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