Question

a circle touches all four sides of a quadrilateral abcd. prove that ab+cd=bc+da
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Answer 1

Answer:

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

Step-by-step explanation:

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