11. If a circle touches all the four sides a quadrilateral ABCD at the

1.	11. If a circle touches all the four sides a quadrilateral ABCD at the points PQRS. Then show thatAB+CD= BC + DA.
Answer» 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.

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

Answer»

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.

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

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