In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = BC + AD.

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CBSE 10th Class Mathematics
Past year question paper
Year 2020
SET 1, Code Number – 30/5/1
Question Number – 24 [b]
Prove that AB + CD = BC + AD
Geometric question
important question for 10th class

Let P, Q, R and S be point of

contact.

AP = AS

BP = BQ

CQ = CR Tangents drawn from external point of circle given in figure

DS = DR

AB + CD = AP + BP + CR + RD

= AS + BQ + CQ + DS

= AS + DS + BQ + CQ

= AD + BC

Hence proved.