What is the maximum number of regions can be formed if you draw six lines across the circle?

31
The maximum number of regions that we can obtain from crossing chords with 6 points is 31. Students quickly realize that if 3 or more chords cross at the same point in the interior of a circle, then they don’t obtain the maximum possible number of regions.

What is the greatest number of regions can 7 lines divide a circle into?

The answer is 22. I’m assuming you mean straight lines. If there are no lines crossing a circle, the number of regions is of course 1.

How many regions N lines divide planes?

One line can divide a plane into two regions, two non-parallel lines can divide a plane into 4 regions and three non-parallel lines can divide into 7 regions, and so on.

How many regions are there in a 7 point circle?

57 regions
If we add a 7th point, and count very carefully, we get 57 regions.

How many points of intersection are formed by N lines drawn in a plane if no two are parallel and no three concurrent into how many regions is the plane divided?

With n lines, there are (n2) intersections (if no two lines are parallel and no three lines are coincident). Thus, the number of regions is (n2)+n+1=n(n−1)2+n+1=n2+n+22. Suppose we draw n straight lines on the plane so that every pair of lines intersects (but no 3 lines intersect at a common point).

How many points of intersection are there in 6 lines?

So, when 6 lines are drawn in a plane, the number of points of intersection to be 10 + 5 = 15.

What is the largest number of regions we can create by drawing 4 lines in a plane?

Leaving that point on one side of the third line means that the line won’t be able to cross all four already existent regions, but at most only three – one more than there are lines. This gives a clue to a general case. In other words, \displaystyle L_{n}=\frac{n(n+1)}{2}+1=\frac{n^{2}+n+2}{2}.