What is the maximum number of nonoverlapping regions into which 3 line

What defines a overlapping region ?

In the diagram, one line makes two regions in the circle. 1 line adds one more region to the region already there (1 + 1 =2).

Two lines add two more regions (to the 2 regions already there, 2 + 2 = 4)); 2 lines create 4 regions.

Three line add three more regions (to the 4 regions already there, 4 + 3 = 7); 3 lines create 7 regions.

The pattern: Each Lth line adds L regions to the number of regions that already existed:

Line (+ line) --- Regions

1 (+ 1st line = adds 1 more region, 1+ 1 = 2) --> 2 regions
2 (+ 2nd line = adds 2 more regions, 2 + 2 = 4) --> 4 regions
3 ( + 3rd line = adds 3 more regions, 4 + 3 + 7) --> 7 regions

I cannot figure out a way to make 8 regions with three lines; and given the pattern, I think it is not possible.

Answer C

Navski , when I drew what you described, I counted six regions.

Looked over it again and it's my fault. You were right, thought I saw 8 for some reason.

Why the third line cannot go through the center of the circle?

Because if it does, it would be 6 regions. We want to look for the maximum, so by not going through the middle, we created a 7th region.

Thank you very much... I did not notice in this way.

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