Question

Draw a pair of tangents inclined to each other at an angle of 60o to a circle of radius 3 cm.

Answer 1

Draw circle as shown in the picture. Draw tangent line AP parallel to radius OE and perpendicular to radius OA at A.
Draw chord EB.  Follow the procedure to trisect BE.  Then join the center and the trisected points to meet circle at C and D.    Angle EOC is 30 deg.
Draw tangent CP at C perpendicular to OC.

PA and PC are tangents desired inclined at 60 deg.