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8.   A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC

       Circles EXERCISE 10.2

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To prove- AB + CD = AD + BC
Proof-
We have,
Since the length of the tangents drawn from an external point to a circle are equal 
AP =AS .......(i)
BP = BQ.........(ii)
AS = AP...........(iii)
CR = CQ ...........(iv)

By adding all the equations, we get;

    AP + BP +RD+ CR = AS +DS +BQ +CQ
\Rightarrow(AP + BP) + (RD + CR) = (AS+DS)+(BQ + CQ)
\RightarrowAB + CD  = AD + BC

hence proved.

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manish

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