A quadrilateral is drawn to circumscribe a circle prove that the sum of opposite sides are equal

A quadrilateral is drawn to circumscribe a circle prove that the sum o

1.	A quadrilateral is drawn to circumscribe a circle prove that the sum of opposite sides are equal
Answer» Since tangents drawn from an exterior point to a circle are equal in length.{tex}\\therefore{/tex} AP = AS [From A] ...(i)BP = BQ [From B] ...(ii)CR = CQ [From C] ...(iii)and, DR = DS [From D] ...(iv)adding (i), (ii), (iii) and (vi), we getAP + BP + CR + DR = AS + BQ + CQ + DS{tex}\\Rightarrow{/tex} (AP + BP) + (CR + DR) = (AS + DS) + (BQ + CQ){tex}\\Rightarrow{/tex} AB + CD = AD + BCHence, AB + CD = BC + DA