How many pieces of a circle can you make by cutting it four times and five times?

Question

So far, this is what i've got :
http://snipurl.com/1s4pp

Can you tell me whats the most you can make?

Thanks.

I prefer you draw a picture, or else give me direct and detailed instructions on how you made your circle.

Answer 1

Good start.

But your 5 line picture is surely not right. Add a fifth line to your 4 line picture that cuts regions 2, 1, 4, 9, and 7, and you should do better.

As for your 4 line solution -- why do the parallel lines have to be parallel? It looks as if you could move them closer together and then let them cross, which for example could create an additional region at the top of what is now region 7.