Question

In Fig. PA and PB are tangents to the circle drawn from an external point P. CD are a third tangent touching the circle at Q. If PB = 10 cm and CQ = 2 cm, what is the length PC?

Answer 1

Given:

PB = 10 cm

CQ = 2 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,

PA = PB = 10 cm (tangent from P)

And,

CA = CQ= 10 cm (tangent from C)

Now,

PC = PA – CA

= 10 cm – 2 cm

= 8 cm

Hence, PC = 8 cm