Question

In the following figure, PA, PC and CD are tangents drawn to a circle of centre O. If AP = 3 cm, CD = 5 cm, then the length of PC is

Answer 1

Answer:

Correct option is

B

5cm

As we know that tangents drawn from any external point (here, it is P) to a circle are equal in length. So,PA=PB.

 1)  CQ=CB=3 cm 

(Since C acts as an external point from where tangents CB & CQ are drawn to the circle, and we know that tangents drawn from any external point to a circle are equal in length, so CQ=CB (similar to the way we proved PA=PB)

2)  PB=PA=8 cm

Now, Since PC+CB=PB=8 cm

=> PC=(8−CB)cm=(8−3)cm=5 cm. 

Hence, Option B is the correct answer.