question_answer

AB and CD are two chords of a circle such that AB = 10 cm, CD = 24 cm and AB||CD. The distance between AB and CD is 17 cm. Then, the radii of the circle is equal to

A)  13 cm 

B)  69 cm

C)  26 cm 

D)  23 cm

Correct Answer: A

Solution :

\[{{r}^{2}}=O{{M}^{2}}+M{{D}^{2}}\] \[{{r}^{2}}={{12}^{2}}+{{x}^{2}}\]                                  ?(i) In \[\Delta OLB,\] \[{{r}^{2}}=L{{B}^{2}}+O{{L}^{2}}\] \[{{r}^{2}}={{(17-x)}^{2}}+{{5}^{2}}\]                 ?(ii) On comparing Eqs. (i) and (ii), \[{{12}^{2}}+{{x}^{2}}=(17-{{x}^{2}})+25\] \[\Rightarrow \]   \[34x=170\] \[\Rightarrow \]   \[x=\frac{170}{34}=5\] \[{{r}^{2}}={{12}^{2}}+{{5}^{2}}=144+25\] \[\Rightarrow \]   \[\,{{r}^{2}}=169\] \[\Rightarrow \]   \[\,r=13\]