Question

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. 8
• B. 20
• C. 28
• D. None of these

Answer 1

The correct option is B

20

Point of intersection of diagonals $n_{C_4}=70$

$\Rightarrow n(n-1)(n-2)(n-3)=70\times 24\Rightarrow n=8$

Total no. of diagonals = $n_{C_2}-n=8_{C_2}-8=20$