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9th Class Mathematics Circles Question Bank Circle

  • question_answer
    In the given figure below. The angle subtended by a chord at its centre is\[\mathbf{12}{{\mathbf{0}}^{{}^\circ }}\], then the ratio between chord and radius is

    A) 1 : 2                             

    B) 1 : 1

    C) \[\sqrt{2}:1\]                      

    D) \[\sqrt{3}:1\]

    Correct Answer: D

    Solution :

    (d): \[OA=OB=r\] units \[\angle AOC={{60}^{{}^\circ }};\text{ }AC=CB\] In \[\Delta AOC\], \[\Rightarrow \]\[sin{{60}^{{}^\circ }}=\frac{Ac}{r}\] \[\Rightarrow \]\[\frac{\sqrt{3}}{2}=\frac{AC}{r}\] \[\Rightarrow \]\[AC=\frac{\sqrt{3r}}{2}\] \[\Rightarrow \]\[AB=2\times \frac{\sqrt{3}r}{2}=\sqrt{3}r\] units \[\therefore \]Required ratio \[=\sqrt{3}:1\]


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