Quantitative Aptitude Ques 1470
Question: Two chords of lengths a m and b m subtend angles $ 60{}^\circ $ and $ 90{}^\circ $ at the centre of the circle, respectively. Which of the following is true?
Options:
A) $ b=\sqrt{2}a $
B) $ a=\sqrt{2}b $
C) $ a=2b $
D) $ b=2a $
Show Answer
Answer:
Correct Answer: A
Solution:
- In $ \Delta AOB, $ $ AO=BO=r $ [radius of circle] $ b^{2}=r^{2}+r^{2} $ $ b=\sqrt{2r^{2}} $
$ \Rightarrow $ $ b=\sqrt{2},r $
(i)
In $ \Delta COD, $
$ \angle COD=60{}^\circ $
Then, $ \angle OCD=\angle ODC $
$ =180{}^\circ -\angle COD $
$ =180{}^\circ -60{}^\circ $
$ =120{}^\circ $
Also, $ \angle OCD=\angle ODC= $ Angle opposite to equal sides.
$ \therefore $ $ \angle OCD=\angle ODC=60{}^\circ $ So, $ \Delta COD $ is equilateral and $ r=a $ … (ii) From Eqs. (i) and (ii), we get $ b=\sqrt{2},a $
BETA
