# Geometry for Middle for schoolers (joining 5 points on a circle)

If there are five points on a circle. How many line segments can be drawn on it, but without overlapping the regions?

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what is a region? –  user4140 Aug 29 '12 at 21:23
Do you care to elaborate on the meaning of "regions"? You have connect the points in a pentagon like this, you can add more line segments, but they intersect like this. Finally, you can connect it all over the place like this. What do you have in mind? –  user2468 Aug 29 '12 at 21:37
You may mean that the line segments join pairs of vertices (the $5$ given points), and that two line segments can only meet at a vertex. Then drawing a few picturs should convince one of the answer, even if in Middle School a proof is difficult to write down. –  André Nicolas Aug 29 '12 at 22:07