# Thread: points on a circle...

1. ## points on a circle...

ok so here is the question...

ok so there are 5 points on a circle, and if two points form a segment, how many segments are there. what is the number of line segments.

this seemed straight forward, i chose my answer to be 7. i made a circle and connected the points careful not to double back, my book says the answer is 10? where did i go wrong?

2. ## Re: points on a circle...

Just list them. Points A, B, C, D, E

AB, AC, AD, AE - 4
BC, BD, BE - 7
CD, CE - 9
DE - 10

I'm not sure what it was you were trying to draw.

3. ## Re: points on a circle...

and you know what there is a pattern. ok the problem said there were 5 points. ok so if i subtract 1 from 5 and then add 4+3+2+1 i get the answer? i thought it was a fluke, but then i tried it on another problem and it worked? can you tell me why this is true? whats actually going on here?

4. ## Re: points on a circle...

When was your last trip through Mathematical Induction?

5. ## Re: points on a circle...

gulps-its been a while. my math is a little rusty, yes i know.

6. ## Re: points on a circle...

Originally Posted by slapmaxwell1
ok so here is the question...

ok so there are 5 points on a circle, and if two points form a segment, how many segments are there. what is the number of line segments.

this seemed straight forward, i chose my answer to be 7. i made a circle and connected the points careful not to double back, my book says the answer is 10? where did i go wrong?
If you have done elementary combinatorics then $\displaystyle {5 \choose 2}=10$ should do it.

7. ## Re: points on a circle...

Originally Posted by slapmaxwell1
gulps-its been a while. my math is a little rusty, yes i know.
OK, without any advanced math technics:

If you have n points than you can draw (n - 1) segments connecting each point with every other point. That means you have

$\displaystyle n \cdot (n-1)$ segments.

Since you have drawn every segment twice you have to divide by 2 to get the correct result:

(n := number of points; s := number of segments)

$\displaystyle s = \dfrac{n \cdot (n-1)}2$

8. ## Re: points on a circle...

thanks again....

Originally Posted by earboth
OK, without any advanced math technics:

If you have n points than you can draw (n - 1) segments connecting each point with every other point. That means you have

$\displaystyle n \cdot (n-1)$ segments.

Since you have drawn every segment twice you have to divide by 2 to get the correct result:

(n := number of points; s := number of segments)

$\displaystyle s = \dfrac{n \cdot (n-1)}2$