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Diagonals Of A Polygon (Posted on 2004-01-31) Difficulty: 2 of 5
A polygon has 1325 diagonals. How many vertices does it have?

No Solution Yet Submitted by Ravi Raja    
Rating: 2.4167 (12 votes)

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re: Common sense | Comment 7 of 16 |
(In reply to Common sense by Jane Doe)

An octagon has 20 diagonals: Each of the 8 vertices can connect to any of 5 of the other vertices (just not to itself nor to either immediate neighbor). So far we've counted 40; but we've counted each one twice--once in each direction, so there are 20. A diagonal of a polygon should not be confused with the diameter of a circle. The latter must go through the center, but the former need not.
  Posted by Charlie on 2004-01-31 13:50:59

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