question_answer

AB and CD are two parallel chords on the opposite sides of the centre of the circle. If AB=10 cm CD = 24 cm and the radius of the circle is 13 cm then what is the distance between the chords?

A)  10 cm             

B)  17 cm

C)  24 cm             

D)  None of these

Correct Answer: B

Solution :

From O draw \[OL\bot AB\]and \[OM\bot CD\] join OA and OC

\[AL=\frac{1}{2},\]\[AB=5\,\,cm,\]\[OA=13\,\,cm\]

\[O{{L}^{2}}=O{{A}^{2}}-A{{L}^{2}}={{(13)}^{2}}-{{(5)}^{2}}\]

\[=(169-25)=144\]

\[\Rightarrow \]\[OL=\sqrt{144}=12\,\,cm\]

Now, \[CM=\frac{1}{2}\times CD=12\,\,cm\] and  \[OC=13\,\,cm\]

\[\therefore \]      \[O{{M}^{2}}=O{{C}^{2}}-C{{M}^{2}}={{(13)}^{2}}-{{(12)}^{2}}\]

\[=(169-144)=25\]

\[\Rightarrow \]   \[OM=\sqrt{25}=5\,\,cm\]

\[\Rightarrow \]   \[ML=OM+OL=(5+12)\,\,cm=17\,\,cm\]