Q. 55.0( 1 Vote )

# In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its sides AB, BC, CD and AD touch the circle at P, Q, R and S respectively.If AB = x cm, BC = 7 cm, CR = 3 cm andAS = 5 cm, find x.

As we know, Tangents drawn from an external point are equal.

CR = CQ [tangents from point C]

CQ = 3 cm [as CR = 3 cm]

Also,

BC = BQ + CQ

7 = BQ + 3 [BC = 7 cm]

BQ = 4 cm

Now,

BP = BQ [tangents from point B]

BP = 4 cm …[1]

AP = AS [tangents from point A]

AP = 5 cm [As AC = 5 cm] ….[2]

AB = AP + BP = 5 + 4 = 9 cm [From 1 and 2]

AB = x = 9 cm

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