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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Tangent and normal to a circle

  • question_answer
    The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}=1\]and \[{{x}^{2}}+{{y}^{2}}-4x+3=0\] is            [DCE 2005]

    A)            1    

    B)            2

    C)            3    

    D)            4

    Correct Answer: C

    Solution :

               Here \[{{C}_{1}}=(0,\,0){{r}_{1}}=1\] unit                    \[{{C}_{2}}=(2,\,0)\,\,{{r}_{2}}=1\]                    Clearly \[{{C}_{1}}{{C}_{2}}={{r}_{1}}+{{r}_{2}}\] \[=1+1=2\]                    Thus two circles touch externally,                    Hence the number of common tangents is 3.


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