Quantitative Aptitude Ques 1129
Question: The length of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at a distance of 4 cm from the centre, then the distance of the other chord from the centre is
Options:
A) 5 cm
B) 6 cm
C) 4 cm
D) 3 cm
Show Answer
Answer:
Correct Answer: D
Solution:
- Length of smaller chord $ =6cm $
$ \therefore $ $ MB=3cm $ and $ OM=4cm $
$ \therefore $ In $ \Delta OMB, $ using Pythagoras theorem $ OB^{2}=OM^{2}+MB^{2}=9+16=25 $
$ \Rightarrow $ $ OB=5cm $ [radius of semi-circle]
$ \therefore $ $ OD=5cm $ $ [\because OB=OD] $ and $ ND=\frac{CD}{2}=\frac{8}{2}=4cm $
$ \therefore $ In $ \Delta OND, $ using Pythagoras theorem $ ON^{2}=OD^{2}-ND^{2} $
$ \Rightarrow $ $ ON^{2}=25-16=9 $
$ \Rightarrow $ $ ON^{2}=3cm $
$ \therefore $ Distance $ =3cm $
BETA
