Quantitative Aptitude Ques 383
Question: AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and distances between them is 17 cm, then the radius of the circle is
Options:
A) 12 cm
B) 13 cm
C) 10 cm
D) 11 cm
Show Answer
Answer:
Correct Answer: B
Solution:
- Let radius of the circle be r. Given, $ MN=17,cm $ Let $ ON=x $ Then, $ OM=17-x $ In $ \Delta AOM, $ $ OA^{2}=OM^{2}+AM^{2} $
$ \Rightarrow $ $ r^{2}={{(17-x)}^{2}}+5^{2} $ $ =289+x^{2}-34x+25 $ $ r^{2}=314+x^{2}-34x $ … (i) In $ \Delta CON, $ $ OC^{2}=ON^{2}+CN^{2} $ $ r^{2}=x^{2}+12^{2}=x^{2}+144 $ … (ii) From Eqs. (i) and (ii), we get $ 314+x^{2}-34x=x^{2}+144 $
$ \Rightarrow $ $ 34x=170 $
$ \Rightarrow $ $ x=5 $
From Eq. (ii),
$ r^{2}=25+144=169 $
$ \Rightarrow $ $ r=13,cm $
BETA
