Answer :
Given:
AB = x cm
BC = 7 cm
CR = 3 cm
AS =5 cm
Property: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal.
By the above property,
AP = AS (tangent from A)
BP = BQ (tangent from B)
CR = CQ (tangent from C)
DR = DS (tangent from D)
Clearly,
QB = CB – CQ
⇒ QB = CB – CR [∵ CQ = CR]
⇒ QB = 7 cm – 3 cm
⇒ QB = 4 cm
Now,
AB = AP + PB
⇒ AB = AS + QB
⇒ AB = 5 cm + 4 cm
⇒ AB = 9 cm
⇒ AB = x = 9 cm
Hence, x = 9 cm
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