How to find chords, intersections of chords on circle?

[Helly123]

Homework Statement

Homework Equations

The Attempt at a Solution

this is the answer

https://www.algebra.com/algebra/homework/Circles/Circles.faq.question.1038060.html

but why the c1 = 0, c2 = 1, c3 = 3, c4 = 6 etc
why not c2 = 2? c4 = 4?

 

[mjc123]

The answer gives you the reasons. What do you not understand about that?

 

[Helly123]

The answer gives you the reasons. What do you not understand about that?

C-n be the number such chords, why there's 0 chords, 1 chords, then suddenly 3 chords, and 6 chords, how you decide that's going to be 3, or 6, 10, 15 , or 1? how do you know the order like that?

 

[mjc123]

Because there are 3 ways of linking 2 points out of 3; 6 ways of linking 2 points out of 4, and so on. You can see that from the diagrams; if you don't know the maths, you can just draw the diagrams and count them. Have you studied the mathematics of combinations - how to choose m things from a set of n things? If not, how come you're doing this problem?

 

[SammyS]

C-n be the number such chords, why there's 0 chords, 1 chords, then suddenly 3 chords, and 6 chords, how you decide that's going to be 3, or 6, 10, 15 , or 1? how do you know the order like that?

Although this thread was marked as being SOLVED, the only solution was in that link and it's clear that you probably do not understand the solution.

There is a somewhat cleaner expression for the number of regions, r_n . You can discover it by considering how r_n is related to c_n and i_n for each case listed in that link.

By The Way;
Are you familiar with Pascal's triangle?