In Fig. CP and CQ are tangents from an external point C to a circle with centre O. AB is another tangent which touches the circle at R.

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In Fig. CP and CQ are tangents from an external point C to a circle with centre O. AB is another tangent which touches the circle at R. If CP = 11 cm and BR = 4 cm, find the length of BC.

Hint: We have, CP = 11 cm

$\therefore$ CP = CQ = CQ = 11 cm

Now, BR = BQ [Tangents drawn from B)

$\Rightarrow BQ=4$ cm

$\therefore$ BC = CQ - BQ = (11 - 4)cm = 7 cm

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Given:

BR = 4 cm

CP = 11 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,

BR = BQ = 4 cm (tangent from B)

And,

CP = CQ = 11 cm (tangent from C)

Now,

BC = CQ – BQ

= 11 cm – 4 cm

= 7 cm

Hence, BC = 7 cm