Solution:

Steps to construct:

Step 1: Draw a circle with center O and radius 4cm and mark that point as A.

Step 2: Take a point P such that OP = 7cm.

Step 3: Bisect OB at M.

Step 4: With center M and diameter OP, draw another circle intersecting the given circle at A and B.

Step 5: Join PA and PB. Hence PA and PB are pair of tangents to the circle.

Step 6: On measuring PA, it is equal to 5.5cm.