Question

In a quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

Answer 1

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According to the Question

Suppose the Quadrilateral ABCD drawn to Circumscribe a circle

The circle touches the side AB , BC , CD and DA

Hence

Length of 2 tangent drawn from an external point of circle are equal

AP = AS

BP = BQ

DR = DS

CR = CQ

Adding all the above we will get :-

(AP + BP)  + (CR + RD) = (BQ + QC) + (DS + SA)

AB + CD = BC + DA

PROVED

REASON = When you add AP and BP you will get AB and Similarly all above.