Question

How many chords can be drawn through 11 points on a circle?

Answer 1

11 chords

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Answer 2

$\huge{\sf \fbox{Solution :}}$

For drawing one chord on a circle , only 2 points are required

Therefore , the combination of 11 points take 2 at a time

$\sf \hookrightarrow Total \: number \: of \: chords = {}^{11} C_{2} \\ \\ \sf \hookrightarrow Total \: number \: of \: chords = \frac{11!}{2!(11 - 2)!} \\ \\ \sf \hookrightarrow Total \: number \: of \: chords = \frac{11!}{2! \times 9!} \\ \\ \sf \hookrightarrow Total \: number \: of \: chords = \frac{11 \times 10 \times 9!}{2 !\times 9!} \\ \\ \sf \hookrightarrow Total \: number \: of \: chords = \frac{110}{2 \times 1} \\ \\ \sf \hookrightarrow Total \: number \: of \: chords = 55$

Hence , 55 chords can be drawn through 11 points on a circle