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  • Area of the circle in which a chord of length makes an angle <img alt="\pi / 2" src="https://entrancecorn

Area of the circle in which a chord of length \sqrt{2} makes an angle \pi / 2 at the centre is

Option: 1

\pi / 2


Option: 2

2 \pi


Option: 3

\pi


Option: 4

\pi / 4


Answers (1)

best_answer

Let \mathrm{AB} be the chord of length ,\mathrm{O}  be the centre of the circle and let \mathrm{OC}  be the perpendicular from \mathrm{O} on \mathrm{AB}. Then \mathrm{AC}=\mathrm{BC}=\sqrt{2} / 2=1 / \sqrt{2}

In \triangle O B C, \mathrm{OB}=\mathrm{BC} \operatorname{cosec} 45 \mathrm{o}=(1 / \sqrt{2}) \times \sqrt{2}=1

Area of the circle =\square(\mathrm{OB}) 2=\pi

Posted by

Gautam harsolia

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