9th Class Mathematics Circles Question Bank Circle

  • question_answer
    In the given figure below. The length of a tangent from an external, point to a circle is \[5\sqrt{3}\] unit. if radius of the circle m 5 units, then the distance of the point from the circle is

    A)  5 units             

    B)  15 units

    C)  -5 units                        

    D)  -15 units

    Correct Answer: A

    Solution :

    (a): \[XY=5\sqrt{3}\]units OX = 5 units \[\angle OXY={{90}^{{}^\circ }}\] \[\therefore \]\[OY=\sqrt{X{{Y}^{2}}+O{{X}^{2}}}\] \[=\sqrt{{{\left( 5\sqrt{3} \right)}^{2}}+{{5}^{2}}}\] \[=\sqrt{75+25}\] \[=\sqrt{100}=10\]units \[\therefore \]\[YZ=OY-OZ\] \[=10-5=5\]units           


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