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 \[\Delta OEA\] |
\[AE=\sqrt{A{{O}^{2}}-O{{E}^{2}}}=\sqrt{{{(15)}^{2}}-{{(12)}^{2}}}\] |
\[\Rightarrow \] \[AE=9\,\,cm\] |
\[\therefore \] \[AB=9\times 2=18\,\,cm\] |
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