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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
Solution
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 = BP = 4 cm ...(2)
AB = AP + PB = (5 + 4) cm = 9 cm
⇒ x = 9 cm
Hence, the correct option is B.
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