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In a polygon no three diagonals are concurrent, if the total number of points of intersection of diagonals interior to the polygon be 70 then the number of diagonals of the polygon is
- a)20
- b)28
- c)8
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a polygon no three diagonals are concurrent, if the total number of...
A selection of four vertices of the polygon gives an interior intersection.
∴ the number of sides = n
⇒ nC4 = 70
⇒ n(n-1)(n-2)(n-3) = 24 x 70 = 8 x 7 x 6 x 5
⇒ n = 8
∴ the number of diagonals =8C2- 8
∴ the number of sides = n
⇒ nC4 = 70
⇒ n(n-1)(n-2)(n-3) = 24 x 70 = 8 x 7 x 6 x 5
⇒ n = 8
∴ the number of diagonals =8C2- 8
Most Upvoted Answer
In a polygon no three diagonals are concurrent, if the total number of...
A selection of four vertices of the polygon gives an interior intersection.
∴ the number of sides = n
⇒ nC4 = 70
⇒ n(n-1)(n-2)(n-3) = 24 x 70 = 8 x 7 x 6 x 5
⇒ n = 8
∴ the number of diagonals =8C2- 8
∴ the number of sides = n
⇒ nC4 = 70
⇒ n(n-1)(n-2)(n-3) = 24 x 70 = 8 x 7 x 6 x 5
⇒ n = 8
∴ the number of diagonals =8C2- 8
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Community Answer
In a polygon no three diagonals are concurrent, if the total number of...
A selection of four vertices of the polygon gives an interior intersection.
∴ the number of sides = n
⇒ nC4 = 70
⇒ n(n-1)(n-2)(n-3) = 24 x 70 = 8 x 7 x 6 x 5
⇒ n = 8
∴ the number of diagonals =8C2- 8
∴ the number of sides = n
⇒ nC4 = 70
⇒ n(n-1)(n-2)(n-3) = 24 x 70 = 8 x 7 x 6 x 5
⇒ n = 8
∴ the number of diagonals =8C2- 8
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In a polygon no three diagonals are concurrent, if the total number of points of intersection of diagonals interior to the polygon be 70 then the number of diagonals of the polygon isa)20b)28c)8d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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