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9th Class Mathematics Circles Question Bank Circle

  • question_answer
    In the given figure below, Chords AB and CD of a circle intersect at E and are perpendicular to each other. Segments AE, EB and ED are of lengths 2 cm, 6 cm and 3 cm respectively. Then the length of the diameter of the circle (in cm) is

    A)  \[\sqrt{65}\]      

    B)  \[\frac{1}{2}\sqrt{65}\]         

    C)  65                               

    D)  \[\frac{65}{2}\]

    Correct Answer: A

    Solution :

    (a): \[AE=2cm\] \[EB=6cm\] \[ED=3cm\] \[\therefore \] \[AE\times EB=DE\times EC\] \[\Rightarrow \] \[EC=\frac{2\times 6}{3}=4cm\] \[\therefore \] Diameter \[=\sqrt{{{7}^{2}}+{{4}^{2}}}\text{= }\sqrt{49+16}\] \[=\sqrt{65}\text{ }cm\]            


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