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9th Class Mathematics Circles Question Bank Circle

  • question_answer
    ABCD is a quadrilateral, the sides of which touch a circle. Which one of the following is correct?

    A)  \[AB+AD=CB+CD\]          

    B)  \[AB:CD=AD:BC\]

    C)  \[AB+CD=AD+BC\]  

    D)  \[AB:AD=CB:CD\]

    Correct Answer: C

    Solution :

    (c):- We know that, two tangents drawn from an external point to a circle are of equal lengths. \[AP=AS\Rightarrow BP=BQ\] \[CR=CQ\Rightarrow DR=DS\] \[\Rightarrow \] \[AP+BP+CR+DR=AS+BQ+CQ+DS\] \[\therefore \] \[AB+CD=AD+BC\]       


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