Q23 of 34 Page 1

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


To prove: AB + CD = AD + BC.



Proof: AS = AP ( Length of tangents from an external point to a circle are equal)


BQ = BP


CQ = CR


DS = DR


AS + BQ + CQ + DS = AP + BP + CR + DR


(AS + DS) + ( BQ + CQ) = (AP + BP) + (CR + DR)


AD + BC = AB +CD


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