Question

Let there be $9$ fixed points on the circumference of a circle. Each of these points is joined to every one of the remaining $8$ points by a straight line and the points are so positioned on the circumference that atmost $2$ straight lines meet in any interior point of the circle. The number of such interior intersection points is

• A. $126$
• B. $151$
• C. $120$
• D. $250$

Answer 1

Answer: (A)

$126$

We'll have to find total number of intersection points.

A point will be formed when two lines intersect i.e. it will involve $4$ points on the circumference of the circle to create $1$ intersecting point.

Hence total number of intersecting points $={}^9{C}_4$

Hence correct answer is $126$