Quantitative Aptitude Ques 1826
Question: Two parallel chords are drawn in a circle of diameter 30 cm. The length of one chord is 24 cm and the distance between the two chords is 21 cm. The length of the other chord is
Options:
A) 10 cm
B) 18 cm
C) 12 cm
D) 16 cm
Show Answer
Answer:
Correct Answer: B
Solution:
- In $ \Delta DFC, $ by Pythagoras theorem $ OF^{2}=OC^{2}-CF^{2} $ and $ CF=\frac{CD}{2} $
$ \Rightarrow $ $ OF=\sqrt{{{(15)}^{2}}-{{(12)}^{2}}} $
$ \Rightarrow $ $ OF=\sqrt{255-144}=9cm $
$ \therefore $ $ OE=21-9=12cm $ $ [\because OE=EF-OF] $ Now, in $ \Delta OEA $ $ AE=\sqrt{AO^{2}-OE^{2}}=\sqrt{{{(15)}^{2}}-{{(12)}^{2}}} $
$ \Rightarrow $ $ AE=9cm $
$ \therefore $ $ AB=9\times 2=18cm $
BETA
