If there are five points on a circle. How many line segments can be drawn on it, but without overlapping the regions?
Geometry for Middle for schoolers (joining 5 points on a circle)
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$\begingroup$
geometry
circles
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1what is a region? – 2012-08-29
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2Do you care to elaborate on the meaning of "regions"? You have connect the points in a pentagon like [this](http://etc.usf.edu/clipart/43400/43444/5c_43444_mth.gif), you can add more line segments, but they intersect like [this](http://www.opentutorial.com/images/thumb/3/32/5star-24-euclid.png/400px-5star-24-euclid.png). Finally, you can connect it all over the place like [this](http://www.zefdamen.nl/CropCircles/Reconstructions/2003/GreenStreet03/greenstreet10.gif). What do you have in mind? – 2012-08-29
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0You 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. – 2012-08-29