Seven points are marked on the circumference of a circle. How many different chords can be drawn by connecting two of these seven points?

 Aug 31, 2020

The number of possible chords is 28.

 Aug 31, 2020

Instead of circles and whatnot, we can instead call this a "heptagon"


AKA this shape:


Anyways, we can reword this question: How many diagonals / sides does a 7-sided heptagon have?


Sure, you can go draw all the lines. I'll wait for you. But there is a quicker, mathematical way to do it.


We see that there are 7 dots to choose from. From these 7 points, how many more points can we use to choose the second dot? There are 7 - 1 = 8 points (because you can't your original point)


Now, we multiply:


7 x 8 = 56


But, remember, the order does not matter! This means that we need to divide by 2! to cancel out the repeats.


56/2! = 56/2 = 28 diagonals / chords       <------ answer that guest got!


have you finished drawing the lines yet? if i were you, i would not draw 28 lines!



 Aug 31, 2020
edited by ilorty  Aug 31, 2020

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