Question

a circle touches all the four sides of a quadrilateral abcd prove that ab+cd=bc+da

Answer 1

From the figure we observe that,

DR = DS (Tangents on the circle from point D) … (i)

AP = AS (Tangents on the circle from point A) … (ii)

BP = BQ (Tangents on the circle from point B) … (iii)

CR = CQ (Tangents on the circle from point C) … (iv)

Adding all these equations,

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

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

⇒ CD + AB = AD + BC

Answer 2

Their u go.... Hope it will work...