How many chords can be drawn through 21 points on a circle?

Solution:
A chord can be drawn by joining any two points on a circle. Therefore, the number of chords that can be drawn out of 21 points is ²¹C₂, which is given by 

²¹C₂ = 21! / 2!19! = 21*20*19! / 2*19! = 210

Thus, the number of chords is 210.

We know that, chord is the line segment joining any two points on the circumference of a circle. 

∴ Number of chords is equal to the number of ways in which we can choose 2 points out of 21 points. 

∴ Required number of chords

= ²¹C₂

= (21 x 20)/(2 x 1) = 210

To draw a chord we need two points on a circle. 

∴ Number chords through 21 points on a circle 

= ²¹C₂ = \(\frac{21\times20}{2\times1}\) = 210

Since, for drawing a chord, we need two different points on circle.

Therefore, total number of chords can be drawn through 21 points on a circle in 

\(^{21}C_2=\cfrac{21\times20\times19!}{19!\times2}\)

= 21 x 10 = 210