UPSC 2016 CDS II Math Paper

ABCD is a quadrilateral whose sides AB, BC, CD and DA touches the circle at points P, Q, R and S, respectively.
Remember: The lengths oftangents drawn from an external point to a circle are equal.
∴ AP = AS ....(1)
PB = BQ ......(2)
DR = DS ......(3)
CR = CQ ......(4)
Adding (1), (2), (3) and (4), we have
(AP + PB) + (CR + DR)
= (AS + DS) + (BQ + CQ)
⇒ AB + CD = AD + BC