9th Class Mathematics Circles Question Bank Circles

  • question_answer
    In the given figure, O is the centre of the circle. The angle subtended by the arc BCD at the centre is 140°. If BC is produced to P, find \[\angle DCP.\]

    A) \[60{}^\circ \]       

    B) \[110{}^\circ \]

    C) \[70{}^\circ \]     

    D) \[80{}^\circ \]

    Correct Answer: C

    Solution :

    \[\angle BAD=\frac{1}{2}\angle BOD=\frac{1}{2}\times {{140}^{o}}={{70}^{o}}\] \[\angle DCP=\angle BAD\][Since exterior angle of a cyclic quadrilateral is equal to the interior opp. angle.] \[\therefore \]\[\angle DCP=\angle BAD={{70}^{o}}\]


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