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9th Class Mathematics Circles Question Bank Circles

  • question_answer
    In the given figure,\[\Delta ABC\]is inscribed in a circle. The bisector of\[\angle BAC\]meets BC at D and the circle at E. If EC is joined and \[\angle ECD={{30}^{o}},\]find \[\angle BAC.\]

    A) \[30{}^\circ \]                          

    B) \[40{}^\circ \]      

    C) \[50{}^\circ \]           

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

    Correct Answer: D

    Solution :

    Since angles in the same segment are equal,  \[\angle BCE=\angle BAE={{30}^{o}}.\] Since, AD is bisector, \[\angle BAE=\angle CAE={{30}^{o}}\] \[\therefore \]\[\angle BAC={{30}^{o}}+{{30}^{o}}={{60}^{o}}\]


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