Q24 of 40 Page 1

In Fig. 4, a circle touches all the four sides of a quadrilateral ABCD. If AB = 6 cm, BC = 9cm, and CD = 8 cm, then find the length of AD.


Given

AB = 6 cm


BC = 9 cm


CD = 8 cm


AD = ?



We know that tangents drawn from an external point to a circle are equal.


∴ AP = AS …(1)


BP = BQ …(2)


DR = DS …(3)


CR = CQ …(4)


Adding equation (1), (2), (3) and (4)


(AP + BP) + (DR + CR) = AS + BQ + DS + CQ


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


AB + CD = AD + BC


Now, 6 + 8 = AD + 9


⇒ AD = 14 – 9 = 5 cm


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