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 and
AS = 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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