question_answer

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                                  [SSC (10+2) 2013]

A) 5 cm                            

B) 6 cm  

C) 4 cm                            

D) 3 cm

Correct Answer: D

Solution :

Length of smaller chord \[=6\,\,cm\]

\[\therefore \]      \[MB=3\,\,cm\]

and       \[OM=4\,\,cm\]

\[\therefore \]In \[\Delta OMB,\]using Pythagoras theorem

\[O{{B}^{2}}=O{{M}^{2}}+M{{B}^{2}}=9+16=25\]

\[\Rightarrow \]   \[OB=5\,\,cm\]   [radius of semi-circle]

\[\therefore \]      \[OD=5\,\,cm\]   \[[\because OB=OD]\]

and       \[ND=\frac{CD}{2}=\frac{8}{2}=4\,\,cm\]

\[\therefore \]In \[\Delta OND,\] using Pythagoras theorem

\[O{{N}^{2}}=O{{D}^{2}}-N{{D}^{2}}\]

\[\Rightarrow \]   \[O{{N}^{2}}=25-16=9\]

\[\Rightarrow \]   \[O{{N}^{2}}=3\,\,cm\]

\[\therefore \]Distance \[=3\,\,cm\]