A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA

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A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA.

Answer

Here AP = AS

BP = BQ

CR = CQ

DR = DS

Adding,

(AP + PB) + (CR + RD) = (AS + SD) + (BQ + QC)

AB + CD = AD + BC

• Exam Year: 2017