Circle And System Of Circles Question 169
Question: Area of the circle in which a chord of length $ \sqrt{2} $ makes an angle $ \frac{\pi }{2} $ at the centre is
Options:
A) $ \frac{\pi }{2} $
B) $ 2\pi $
C) $ \pi $
D) $ \frac{\pi }{4} $
Show Answer
Answer:
Correct Answer: C
Solution:
Let AB be the chord of length $ \sqrt{2} $ , O be centre of the circle and let OC be the perpendicular from O on AB.
Then $ AC=BC=\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}} $
In $ \Delta \ OBC,\ OB=BC,\text{cosec }45^{o}=\frac{1}{\sqrt{2}}.\sqrt{2}=1 $
$ \therefore $ Area of the circle $ =\pi {{(OB)}^{2}}=\pi $ .
BETA
