A) 17 cm
B) 15 cm
C) 16 cm
D) 18 cm
Correct Answer: A
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 |
\[O{{L}^{2}}=O{{A}^{2}}-A{{L}^{2}}={{(13)}^{2}}-{{5}^{2}}=(169-25)=144\] \[\Rightarrow \] \[OL=\sqrt{144}=12\,\,\text{cm}\] |
Now, \[A{{B}^{2}}=O{{A}^{2}}+O{{B}^{2}}={{(12)}^{2}}+{{9}^{2}}=(144+81)=225\]and \[OC=13\,\,\text{cm}\] |
\[\therefore \]\[O{{M}^{2}}=O{{C}^{2}}-C{{M}^{2}}={{(13)}^{2}}-{{(12)}^{2}}=(169-144)=25\] |
\[\Rightarrow \] \[OM=\sqrt{25}=5\,\,\text{cm}\] |
\[\therefore \] \[ML=OM+OL=(5+12)\,\,\text{cm}=17\,\,\text{cm}\] |
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