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9th Class Mathematics Circles Question Bank Circle

  • question_answer
    In the given figure below, two chords AB and CD of a circle with centre O intersect at P. If \[\angle \mathbf{APC}=\mathbf{3}{{\mathbf{0}}^{{}^\circ }}\]. Then the value of \[\angle \mathbf{AOC}+~\angle \mathbf{BOD}\] is

    A)  \[{{50}^{{}^\circ }}\]                          

    B)  \[{{60}^{{}^\circ }}\]

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

    D)  \[{{120}^{{}^\circ }}\]

    Correct Answer: D

    Solution :

    (d): Arc AC subtends \[\angle AOC\] at the centre and \[\angle ABC\] at the circumference. Similarly, \[\angle BOD=2\angle BCD\] \[\therefore \] \[\angle AOC+\angle BOD\] \[=2\left( \angle ABC+\angle BCD \right)\] \[=2\angle APC=2\times {{30}^{{}^\circ }}={{60}^{{}^\circ }}\]


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