Q. 44

# Quadrilateral ABCD is circumscribed to a circle. If AB = 6 cm, BC = 7 cm and CD = 4 cm then the length of AD isA. 3 cmB. 4 cmC. 6 cmD. 7 cm 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,

So, 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 …

BC = 7 cm

BP + CP = 7

x + y = 7 …

CD = 4 cm

CR + DR = 4

y + z = 4 …

Also,

AD = AS + DS = w + z …

Add  and  and substracting  from the sum we get,

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

w + z = 3 cm

From 

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