Question

How many chords can be drawn through 12 points on a circle?

Answer 1

The answer is 66 .

There are 12 points and 2 points constitute a chord.

So the no. Of chords that can we draw through 12 points in a circle=¹²C2

Answer 2

As we know a combination is calculated as,

$^nC_r=\frac{n!}{(n-r)!r!}$

Given : 12 points on a circle.

A chord requires two points.

$^{12}C_2=\frac{12!}{(12-2)!2!}$

$^{12}C_2=\frac{12\times 11\times 10!}{(10)!2!}$

$^{12}C_2=\frac{12\times 11}{2}$

$^{12}C_2=\frac{132}{2}$

$^{12}C_2=66$

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