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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank System of circles

  • question_answer
    The condition that the circle \[{{(x-3)}^{2}}+{{(y-4)}^{2}}={{r}^{2}}\]lies entirely within the circle \[{{x}^{2}}+{{y}^{2}}={{R}^{2}},\]is               [AMU 1999]

    A)            \[R+r\le 7\]                               

    B)            \[{{R}^{2}}+{{r}^{2}}<49\]

    C)            \[{{R}^{2}}-{{r}^{2}}<25\]   

    D)          \[R-r>5\]

    Correct Answer: D

    Solution :

               Clearly, \[{{r}_{1}}-{{r}_{2}}>{{C}_{1}}{{C}_{2}}\]                    \[{{r}_{1}}=R,\] \[{{C}_{1}}(3,\,4);\] \[{{r}_{2}}=r;\]\[{{C}_{2}}(0,\,0)\]                    \[R-r>\sqrt{{{(3-0)}^{2}}+{{(4-0)}^{2}}}\]Þ R ? r > 5.


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