Question

11. If a circle touches all the four sides a quadrilateral ABCD at the points PQRS. Then show that
AB+CD= BC + DA.​

Answer 1

Step-by-step explanation:

Lengths of the tangents from an external point are equal.

AP = AS, BP = BQ, CR = CQ and DR = DS

AB + CD = (AP + BP) + (CR + DR)

= AS + BQ + CQ + DS

= (AS + DS) + (BQ + CQ)

= AD + BC

Hence AB + CD = AD + BC.