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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 each other at P. If \[\angle \mathbf{AOD}=\mathbf{12}{{\mathbf{0}}^{{}^\circ }}\]and \[\angle \mathbf{BOC}=\mathbf{5}{{\mathbf{0}}^{{}^\circ }}\], then the value of \[\angle \mathbf{APC}\] is

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

    B)  \[{{75}^{{}^\circ }}\]

    C)  \[{{85}^{{}^\circ }}\]                                   

    D)  \[{{95}^{{}^\circ }}\]

    Correct Answer: D

    Solution :

    (d): \[\angle AOD={{120}^{{}^\circ }}\] \[\angle ACD=\angle ACP=\frac{120}{2}={{60}^{{}^\circ }}\] (The angle subtended at the centre is twice to that, of angle at: the circumference by the same arc) Again \[\angle BOC={{50}^{{}^\circ }}\] \[\therefore \] \[\angle BAC=\frac{50}{2}={{25}^{{}^\circ }}=\angle PAC\] \[\therefore \] \[\angle APC={{180}^{{}^\circ }}-{{60}^{{}^\circ }}-25={{95}^{{}^\circ }}\]


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