Question

A quadrilateral ABCD is drawn to circumscribe a circle such that it's sides AB, BC, CD, and AD touch the circle at P, Q, R and S respectively if AB=x cm BC equals to 7cm CR equals to 3cm and AS equals to 5cm then x ​

Answer 1

》We already know that tangents from a single exterior point are equal in length.

Hence,

BQ = BP

CQ = CR

DR = DS

and

AS = AP = 5cm

⟹ BQ + CQ = 7 cm

⟹ BQ + CR = 7cm

BQ=4cm

⟹ BQ = BP = 4cm

⟹ AB = x

⟹ BP + AP = 5 + 4 = 9cm

X = 9 cm

Answer 2

Answer:

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Given,

BC = 7cm

CR = 3cm

AS = 5cm

AB = X cm

Now, BQ = BP ( The lengths of the tangents drawn from an external point to a circle are equal)

AP = AS = 5cm

Similarly we have :

CR = CQ = 3cm

BQ = BC - CQ and BC = 7cm (Given)

⇨BQ = (7 - 3) = 4cm

⇨BQ = BP = 4cm

From (1) and (2) we have:

AB = AP + PB (5+4) cm = 9cm

⇨ X = 9cm