Q. 94.4( 24 Votes )

In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.


Answer :

Let sides AB, BC, CD, and AD touches circle at P, Q, R and S respectively.



As we know that tangents drawn from an external point to a circle are equal,


In the given image we have,


AP = AS = w (say) [Tangents from point A]


BP = BQ = x (say) [Tangents from point B]


CP = CR = y (say) [Tangents from point C]


DR = DS = z (say) [Tangents from point D]


Now,


Given,


AB = 6 cm


AP + BP = 6


w + x = 6 …[1]


BC = 7 cm


BP + CP = 7


x + y = 7 ….[2]


CD = 4 cm


CR + DR = 4


y + z = 4 ….[3]


Also,


AD = AS + DS = w + z ….[4]


Add [1] and [3] and substracting [2] from the sum we get,


w + x + y + z - (x + y) = 6 + 4 - 7


w + z = 3 cm ; From [4]


AD = 3 cm


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