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9th Class Mathematics Circles Question Bank Circles

  • question_answer
    In the given figure, O is the centre of the circle. PQ is a chord of the circle and R is any point on the circle. If \[\angle PRQ=l\]and\[\angle OPQ=m,\]what is the value of\[l+m?\]

    A)  Greater than \[90{}^\circ \]

    B)  Less than \[90{}^\circ \]

    C)  Equal to \[180{}^\circ \]

    D)  Equal to \[90{}^\circ \]

    Correct Answer: D

    Solution :

    \[\angle POQ=2\angle R\Rightarrow \angle POQ=2l\] In \[\Delta PQO,OP=OQ=r\] \[\Rightarrow \]\[\angle OQP=\angle OPQ=m\] Also, \[\angle OPQ+\angle OQP+\angle POQ={{180}^{o}}\] \[\Rightarrow \]\[m+m+2l={{180}^{o}}\] \[\Rightarrow \]\[m+l={{90}^{o}}\]


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