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

1.	A quadrilateral is drawn to circumscribe a circle.Prove that AB+CD=AD+BC
Answer» We know that the tangent segments from an external point to a circle are equal\xa0{tex}\\therefore{/tex} AP = AS ........(1)BP = BQ .......(2)CR = CQ .......(3)DR = DS .......(4)Adding (1), (2), (3) and (4), we get(AP + BP) + (CR + DR) = (AS + BQ + CQ + DS){tex}\\Rightarrow{/tex}\xa0AB + CD = (AS + DS) + (BQ + CQ){tex}\\Rightarrow{/tex}\xa0AB + CD = AD + BC

Discussion