question_answer

The lengths of two parallel chords of a circle of radius 5 cm, are 6 cm and 8 cm in the same side of the centre. The distance between them is                                                                                      [SSC (10+2) 2014]

A) 1.5 cm             

B) 1 cm

C) 3 cm                            

D) 2 cm

Correct Answer: B

Solution :

Here, r = 5 cm, AB = 8 cm

\[\therefore \]  AN = NB = 4cm, CD = 6cm

\[\therefore \] CM = MD = 3cm

In \[\Delta ONB,\]\[O{{B}^{2}}=O{{N}^{2}}+N{{B}^{2}}\]

\[{{5}^{2}}=O{{N}^{2}}+{{4}^{2}}\]

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

\[\Rightarrow \]   \[ON=3cm\]

In \[\Delta OMD,\]\[O{{D}^{2}}=O{{M}^{2}}+M{{D}^{2}}\]

\[\Rightarrow \]   \[{{5}^{2}}={{(ON+MN)}^{2}}+{{3}^{2}}\]

\[\Rightarrow \] \[{{(3+MN)}^{2}}=25-9=16\]

\[\Rightarrow \]   \[3+MN=4\]

\[\therefore \]      \[MN=4-3=1\,cm\]