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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 positioned on the circumference so that at most 2 of the aformentioned lines meet in any interior point of the circle, as shown in the example below. How many intersection points are there

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 positioned on the circumference so that at most 2 of the aformentioned lines meet in any interior point of the circle, as shown in the example below. How many intersection points are there

Grade:11

1 Answers

Anindya Ranjan
28 Points
6 years ago
It is a good question from the topic ‘Combination’, it’s soln. is as following:
For an intersection point, by the hypothesis that- this point is an intersection of two line segments, tells us that there must be two line segments consisting of 4 fixed points of the circle for an intersection point.
Thus,total no. of intersection points = total no. of ways we can select 4 fixed points from the 9 fixed points = 9C4 = 126

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