Question:medium

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

Updated On: Jan 27, 2026
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Solution and Explanation

For drawing one chord on a circle, only 2 points are required. 
To know the number of chords that can be drawn through the given 21 points on a circle, the number of combinations have to be counted. 
Therefore, there will be as many chords as there are combinations of 21 points taken 2 at a time. 

Thus, required number of chords 
\(=\space^{21}C_2=\frac{2!}{2!\left(21-2\right)!}\)

\(=\frac{21!}{2!19!}\)

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

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