Q.

In a polygon, no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon is 70, then the number of diagonals of the polygon is

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a

20

b

28

c

8

d

none of these

answer is A.

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Detailed Solution

Let the number of sides be n. A selection of four vertices of the polygon gives an interior point of intersection of diagonals ∴ nC4=70⇒ n(n−1)(n−2)(n−3)=24×70=8×7×6×5⇒ n=8
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