9th Class Mathematics Circles Question Bank Circles

  • question_answer
    In the given figure, O is the centre of a circle having radius 5 cm. If \[OM\bot PQ\]and OM = 3 cm, find the length of chord PQ.

    A)  5 cm                          

    B)  8 cm 

    C)  10 cm            

    D)    6 cm

    Correct Answer: B

    Solution :

    \[OM\bot PQ\] \[\Rightarrow \]M is the mid-point of PQ Join OQ. Now, in rt. \[\Delta {\mathrm O}\Mu Q,\]we have \[M{{Q}^{2}}=O{{Q}^{2}}-O{{M}^{2}}\] \[\Rightarrow \]\[MQ=\sqrt{16}=4\,cm\] \[\therefore \]\[PQ=2\times MQ=2\times 4=8\,cm\]


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