Question

In Figure 1, 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.

(A) 10
(B) 9
(C) 8
(D) 7

Answer 1

Given:
BC = 7 cm
CR = 3 cm
AS = 5 cm
AB = x cm

Now, BQ = BP  (The lengths of the tangents drawn from an external point to a circle are equal.)
AP = AS = 5 cm               ...(1)
Similarly, we have:
CR = CQ = 3 cm

BQ = BC \[-\] CQ and BC = 7 cm (Given)

⇒ BQ = (7 −- 3) cm = 4 cm
⇒ BQ = BP = 4 cm           ...(2)

From (1) and (2), we have:
AB = AP + PB = (5 + 4) cm = 9 cm
⇒ x = 9 cm

Hence, the correct option is B.