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

  • question_answer
    P, Q and R are the centres and \[{{r}_{1}},\,\,{{r}_{2}},\,\,{{r}_{3}}\] are the radii respectively of three co-axial circles, then \[QRr_{1}^{2}+RP\,r_{2}^{2}+PQr_{3}^{2}\] is equal to

    A)            \[PQ\ .\,QR\,.\,RP\]                   

    B)          \[-PQ\,.\,QR\,.\,RP\]

    C)            \[P{{Q}^{2}}.Q{{R}^{2}}.R{{P}^{2}}\]                        

    D)            None of these

    Correct Answer: B

    Solution :

               As\[\Sigma g_{1}^{2}({{g}_{2}}-{{g}_{3}})=-({{g}_{1}}-{{g}_{2}})({{g}_{2}}-{{g}_{3}})({{g}_{3}}-{{g}_{1}})\].


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