10th Class Mathematics Solved Paper - Mathematics 2017 Delhi Set-III

  • question_answer
    In the figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD.   

    Answer:

    Construction: Extend AB and CD to meet at a point P
    Now, PA and PC are tangents of circle with centre O
    So                    \[PA=PC\]                                             ...(i)
    PB and PD are tangent on circle with centre O?
    So                    \[PB=PD\]                                             ...(ii)
    On subtracting eq. (ii) from eq. (i)
        \[PA-PR=PCPD\]
                \[AB=CD\]                                Hence Proved


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