Question

In Fig. 10.103, 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, then x=
A. 10
B. 9
C. 8
D. 7

Answer 1

Answer:

By the property of: Tangents from a single exterior point are equal in length:-

BP = BQ

CQ = CR

DR = DS

AS = AP = 5 cm

=> BQ + CQ = 7

=> BQ + CR = 7 [CQ = CR, proved.]

=> BQ = 4 cm

BQ = BP = 4 cm [proved.]

AB = x = BP + AP = 5 + 4 = 9 cm

Answer:- (b) 9 cm

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Answer 2

$\underline \mathbb{SOLUTION}$

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

$\bold{\huge{\fbox{\color{Red}{Hence,}}}}$

BQ = BP

CQ = CR

DR = DS

and

AS = AP = 5cm

$\implies\:$BQ + CQ = 7 cm

$\implies\:$BQ + CR = 7cm

$\boxed {BQ = 4cm}$

$\implies\:$BQ = BP = 4cm

$\implies\:$ AB = x

$\implies\:$ BP + AP = 5 + 4 = 9cm

$\boxed {X = 9cm}$

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