Question

quadrilateral ABCD is drawn to

circumscribe a circle.

Prove that AB + CD = AD + BC​

Answer 1

Step-by-step explanation:

Hope so that it will be helpful

Answer 2

Step-by-step explanation:

From the Figure,BC, AB,DC, DAare sides of the Quadrilaterals which also form the tangents to the circleinscribed within quadrilateral ABCD.Prove : AB + CD = AD + BCWe know that lengths of tangents drawn from an external point of the circle areequal.DR = DS ………….. (1)CR = CQ ………….. (2)BP = BQ ………….. (3)AP = AS ………….. (4)Add equation (1), (2), (3), (4), we getDR + CR+ BP + AP = DS + CQ + BQ + AS(DR + CR) + (BP + AP) = (DS + AS) + (CQ + BQ) (By regrouping) ————-(5)From the figure,DR +CR = DCBP + AP = ABDS + AS = ADCQ +BQ = BCSubstituting the above values in equation (5),CD + AB = AD + BCHence, proved.