Railways Sample Paper RRBs Assistant Loco Pilot and Technician CBT STAGE-I Sample Paper-28

  • question_answer
    AB and CD are two parallel chords on the opposite sides of the centre of the circle. Lf AB=10 cm, CD = 24 cm and the radius of the circle is 13 cm, the distance between the chords is

    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 cm

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