Steps for construction:

i) Draw a circle with centre O and radius 3 cm.

ii) Take a point P from O, such that OP = 5 cm.

iii) Now, draw a bisector of OP which intersects OP at M.

iv) With centre M, and radius OM, draw a circle which intersects the given circle at A and B.

v) Join AP and BP.

We get, AP and BP are the required tangents.

Therefore, we get AP = BP = 4 cm.