RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 12. Circles

Subject: Maths - Class 10th

Q. No. 5 of Formative Assessment (Unit Test)

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5

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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