question_answer

AB and CD are two chords of a circle such that \[AB=10\]cm, \[CD=24\text{ }cm\]and \[AB||CD\]. The distance between AB and CD is 17 cm. Then, the radius of the circle is equal to

A)  13cm             

B)  169 cm

C)  26 cm                        

D)  None of these

Correct Answer: A

Solution :

Let radius be r, then In \[\Delta OMD,\,{{r}^{2}}=O{{M}^{2}}+M{{D}^{2}}\]             \[{{r}^{2}}={{12}^{2}}+{{x}^{2}}\]             ?..(i) In \[\Delta OLB,\,\,{{r}^{2}}=L{{B}^{2}}+O{{L}^{2}}\] \[{{r}^{2}}={{(17-x)}^{2}}+{{5}^{2}}\]             ...(ii) Comparing of both equations, \[{{12}^{2}}+{{x}^{2}}={{(17-x)}^{2}}+25\] \[43x=170\Rightarrow x=\frac{170}{34}=5\] and       \[{{r}^{2}}={{12}^{2}}+{{5}^{2}}\]             \[=144+25=169\] \[\therefore \]    \[r=13\,cm\]