Number of points $=21$
$\Rightarrow n=21$
A chord connects circle at two points.
$\Rightarrow r=2$

$\therefore$Number of chords from $21$ points on a circle $={}^{n}C_r$
$\therefore {}^{n}C_r={}^{21}C_2$
$=\frac{21!}{19!\times 2!}$
$=\frac{21\times 20\times 19!}{19!\times 2\times 1}$
$=210$ 
 $\therefore$ $210$ chords can be drawn through $21$ points on a circle.