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9th Class Mathematics Circles Question Bank Circles

  • question_answer
    Two chords AB and CD of a circle cut each other when produced outside the circle at P. AD and BC are joined. If \[\angle BAD={{30}^{o}}\]and \[\angle CPA={{45}^{o}},\]find \[\angle CBP.\]

    A) \[105{}^\circ \]                       

    B) \[115{}^\circ \]   

    C) \[135{}^\circ \]

    D) \[75{}^\circ \]

    Correct Answer: A

    Solution :

    Angles in the same segment are equal. \[\Rightarrow \]\[\angle BAD=\angle BCD={{30}^{o}}\] In \[\Delta CBP,\angle C+\angle B+\angle P={{180}^{o}}\] \[\Rightarrow \]\[\angle CBP={{105}^{o}}\]


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