SSC CGL Tier II 25 Oct 2015 Paper 1

(1) Since tangents drawn from an exterior point to a circle are equal in length.
∴ AP = AS
BP = BQ
CR = CQ
DR = DS
On adding all these,
AP + BP + CR + DR = AS + BQ + CQ + DS
⇒ (AP + BP) + (CR + DR) = (AS + DS) + (BQ + CQ)
⇒ AB + CD = BC + DA
⇒ 7 + 9.2 = 8.5 + DA
⇒ 16.2 = 8.5 + DA
⇒ DA = 16.2 – 8.5 = 7.7 cm.