10th Class Mathematics Circles Question Bank Circles

  • question_answer
    In the given figure, ABCD is a cyclic quadrilateral and PQ is tangent to the circle with centre '0'. BD is diameter. \[\angle DCO={{40}^{o}},\] \[\angle ABD={{60}^{o}}\]. Then \[\angle BCP=\] _____.

    A) \[{{50}^{o}}\]               

    B)        \[{{100}^{o}}\]                   

    C)        \[{{60}^{o}}\]                     

    D)        \[{{20}^{o}}\]                     

    Correct Answer: A

    Solution :

    BD is diameter of circle. So, \[\angle DCB={{90}^{o}}.\text{ }QCP\]is a straight line, \[\therefore \]  \[\angle QCP={{180}^{o}}\Rightarrow {{40}^{o}}+{{90}^{o}}+\angle PCB={{180}^{o}}\] \[\Rightarrow \]            \[\angle PCB={{50}^{o}}\]


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