Question

In a convex nonagon all the diagonals are drawn. These diagonals intersect each other at $p$ points inside the nonagon, $q$ points on the nonagon and $r$ points outside the nonagon. Find the maximum possible value of $p$

• A. $124$
• B. $96$
• C. $120$
• D. $126$

Answer 1

Answer: (D)

$126$

We need to find no. of intersection of $2$ internal diagonals in a nanogen i.e. $9$ sided figure.

We need $4$ vertices to allow $2$ diagonals to get point of intersection.

$\Rightarrow$ Total $={}^9{C}_4=\frac{9\times 8\times 7\times 6}{4\times 3\times 2\times 1}$

$=9\times 2\times 7$

$=126.$

Hence, the answer is $126.$