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

Options

A. 8
B. 20
C. 28
D. none of these

Explanation

Let there be n-sides of the polygon. Then, number of vertivces is also n. We know that in a convex polygon every group of four vertices determines two diagonals and hence one point of intersection So. Total numbers of points of interesction of diagonals is `""^(n)C_(4)`.
`:.""^(n)C_(4)=70`
`impliesn(n-1)(n-2)(n-3)=70xx24`
`impliesn(n-1)(n-2)(n-3)=5xx6xx7xx8`
`impliesn=8`
Hence, number of diaonals `=""^(n)C_(2)-n=""^(8)C_(2)-8=20`.