question_answer

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                                   [SSC (CGL) 2012]

A) 10 cm              

B) 18 cm

C) 12 cm              

D) 16 cm

Correct Answer: B

Solution :

In \[\Delta DFC,\]by Pythagoras theorem

\[O{{F}^{2}}=O{{C}^{2}}-C{{F}^{2}}\]

and \[CF=\frac{CD}{2}\]

\[\Rightarrow \]\[OF=\sqrt{{{(15)}^{2}}-{{(12)}^{2}}}\]

\[\Rightarrow \]\[OF=\sqrt{255-144}=9\,\,cm\]

\[\therefore \]\[OE=21-9=12\,\,cm\]

\[[\because OE=EF-OF]\]

Now, in \[\Delta OEA\]

\[AE=\sqrt{A{{O}^{2}}-O{{E}^{2}}}=\sqrt{{{(15)}^{2}}-{{(12)}^{2}}}\]

\[\Rightarrow \]   \[AE=9\,\,cm\]

\[\therefore \]      \[AB=9\times 2=18\,\,cm\]