In Fig. 10.76, 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 CP = CQ = CQ = 11 cm Now, BR = BQ [Tangents drawn from B) BQ = 4 cm BC = CQ - BQ = (11 - 4)cm = 7 cm

Question

Philoid · Accepted Answer

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