Question

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

Answer 1

Given: PA and PB are tangents from external point P; CD is a tangent touching the circle at Q. PB = 10 cm and CQ = 2 cm.

Step-wise calculation:

1. Tangents from the same external point are equal.

So PA = PB = 10 cm.

2. For external point C the two tangents from C are CA and CQ.

So CA = CQ = 2 cm.

3. Point C lies on PA.

So PC = PA – CA

= 10 – 2

= 8 cm