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9th Class Mathematics Circles Question Bank Circle

  • question_answer
    In the given figure below, AB is a chord of a circle with centre O. A tangent AT is drawn at point A so that \[\angle \mathbf{BAT}\text{ }=\mathbf{4}{{\mathbf{0}}^{{}^\circ }}\]. Then \[\angle \mathbf{ADB}=\]?

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

    B)  \[{{130}^{{}^\circ }}\]

    C)  \[{{140}^{{}^\circ }}\]         

    D)  \[{{150}^{{}^\circ }}\]

    Correct Answer: C

    Solution :

    (c): \[\therefore \]\[\angle BAT={{40}^{{}^\circ }}\] \[OA=OB=radii\] \[\angle OAT={{90}^{{}^\circ }}\] \[\therefore \] \[\angle OAB=\angle OBA\] \[={{90}^{{}^\circ }}-{{40}^{{}^\circ }}={{50}^{{}^\circ }}\] \[\therefore \]\[\angle AOB={{80}^{{}^\circ }}\] \[\therefore \] \[\angle AEB=\frac{{{80}^{{}^\circ }}}{2}={{40}^{{}^\circ }}\] ADBE is a cyclic quadrilateral. \[\therefore \] \[\angle ADB={{180}^{{}^\circ }}-{{40}^{{}^\circ }}={{140}^{{}^\circ }}\]             


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