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10th Class Mathematics Circles Question Bank Circles

  • question_answer
    In the given figure, a circle touches the side SC of \[\Delta ABC\]at P and touches AB and /AC produced at Q and R respectively. If \[AQ=5\,cm,\] find the perimeter of \[\Delta ABC\].                                 

    A) 11 cm             

    B)        10 cm                         

    C)        6 cm                           

    D)        7 cm               

    Correct Answer: B

    Solution :

    Perimeter of \[\Delta \,ABC=AB+BC+AC\] \[=AB+(BP+PC)+AC\] \[=(AB+BQ)+(CR+AC)\]                 \[\left\{ \begin{align}   & \because \,\,\,\,\,BP=BQ \\  & PC=CR \\ \end{align} \right\}\] \[=AQ+AR\] (\[\because \]AQ = AR, tangents of circle from same point A) \[=2\text{ }AQ=2\times 5=10\text{ }cm\]


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