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In Fig. CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then find the length of BR.

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Given:

CP = 11 cm

BC = 7 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.

Using the above property,

CP = CQ = 11 cm (tangent from C)

BQ = BR (tangent from B)

And,

AP = AR (tangent from A)

Now, 

BR = BQ = CQ – CB 

= 11 cm – 7 cm 

= 4 cm 

Hence, BR = 4 cm

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