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 be 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 the circle]

\[\therefore \]      \[OD=5\,cm\]

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

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

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

\[=25-16=9\]

\[\Rightarrow \]   \[ON=3\,cm\]

Distance = 3 cm