question_answer

A chord of a circle is 12 cm in length and its distance from the centre is 8 cm. Find the length of the chord of the same circle which is at a distance of 6 cm from the centre.

A)  30 cm            

B)  24 cm

C)  16 cm            

D)    18 cm

Correct Answer: C

Solution :

Given \[AB=12\,cm\Rightarrow AM=MB=6\,cm\] In \[\Delta OMA,O{{A}^{2}}=O{{M}^{2}}+A{{M}^{2}}\] \[\Rightarrow \]\[OA=\sqrt{100}=10\,cm\] \[\therefore \]Radius \[=OA=OC=10\,cm\] In \[\Delta ONC,O{{C}^{2}}=O{{N}^{2}}+N{{C}^{2}}\] \[\Rightarrow \]\[NC=\sqrt{64}=8\,cm\] \[\therefore \]Length of the chord \[=2\times NC=16\,cm\]