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.