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9th Class Mathematics Circles Question Bank Circle

  • question_answer
    In the given figure below, If PX and PY are tangents to the circle with centre O that \[\angle \mathbf{XPY}=\mathbf{4}{{\mathbf{0}}^{{}^\circ }}\], then \[\angle \mathbf{OXY}\] is equal to

    A)  \[{{20}^{{}^\circ }}\] 

    B)  \[{{30}^{{}^\circ }}\]

    C)  \[{{40}^{{}^\circ }}\]                                   

    D)  \[{{50}^{{}^\circ }}\]

    Correct Answer: A

    Solution :

    (a): \[PX=PY\] (tangents from an exterior point) \[OX=OY\] =radii \[\angle XPO=\angle OPY={{20}^{{}^\circ }}\] \[\angle PXY=\angle PYX=\frac{140}{2}={{70}^{{}^\circ }}\] \[\angle OXP={{90}^{{}^\circ }}\] \[\therefore \]\[\angle OXY={{90}^{{}^\circ }}-{{70}^{{}^\circ }}={{20}^{{}^\circ }}\]                              


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