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9th Class Mathematics Circles Question Bank Circles

  • question_answer
    In the figure given, \[\overline{DC}\]is produced to E and if \[\overline{AC}\]is the bisector of\[\angle A,\]find the measure of\[\angle BCD.\]

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

    B) \[160{}^\circ \]    

    C) \[60{}^\circ \]             

    D) \[240{}^\circ \]

    Correct Answer: C

    Solution :

    Since ABCD is a cyclic quadrilateral, \[\angle DAB=\angle BCE={{120}^{o}}.\] Since AC is the bisector of \[\angle DAB,\] \[\angle DAC=\frac{{{120}^{o}}}{2}={{60}^{o}}.\] Since angles in the same segment are equal, \[\angle DBC=\angle DAC={{60}^{o}}.\]


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