Question

If each of three lines intersects a circle at two points, what is the greatest number of separate regions that can be formed?

Answer 1

Answer:

7

Step-by-step explanation:

See the attached diagram with this answer.

If two straight lines cross a circle intersecting at two points then they can form a maximum of 4 regions within the circle, like the straight lines pq and rs form in circle c.

Now, another straight line mn is so placed that it forms the maximum number of separate regions in the circle.

Therefore, from the diagram, it is clear that there may be a maximum 7 separate regions formed by three straight lines intersecting the circle at two distinct points. (Answer)