Q. 474.5( 4 Votes )

In Fig. 10.103, a

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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