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9th Class Mathematics Geometry Question Bank Geometry

  • question_answer
    In the given figure, if C is the centre of the circle and \[\angle PQC=25{}^\circ \] and \[\angle PRC=15{}^\circ \], then \[\angle QCR\] is equal to  

    A) \[40{}^\circ \]

    B) \[60{}^\circ \]

    C) \[80{}^\circ \]  

    D) \[120{}^\circ \]

    Correct Answer: C

    Solution :

      Clearly,      \[CP=CQ\] (Radii of circle) and          \[CR=CP\] \[\therefore \]  \[\angle CPQ={{25}^{o}}\] and      \[\angle CPR={{15}^{o}}\] So that   \[\angle QPR={{40}^{o}}\] Hence,   \[\angle QCR=2\angle QPR\]                 \[=2\times {{40}^{o}}={{80}^{o}}\]


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