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. \[AL=\frac{1}{2}AB=5\,\,cm,OA=13\,\,cm\] \[O{{L}^{2}}=O{{A}^{2}}-A{{L}^{2}}\] \[={{(13)}^{2}}-{{5}^{2}}=169-25=144\] \[\Rightarrow \] \[OL=\sqrt{144}=12\,\,cm\] Now, \[CM=\frac{1}{2}\times CD=12\,\,cm\] and OC = 13 cm \[\therefore \]\[O{{M}^{2}}=O{{C}^{2}}-C{{M}^{2}}={{(13)}^{2}}-{{(12)}^{2}}\] \[=169-144=25\] \[\Rightarrow \]\[OM=\sqrt{25}=5\,\,cm\] \[\therefore \]ML = OM +OL = (5+12) cm = 17 cmYou need to login to perform this action.
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