Draw the given circles with centres O and P and radii R_{1} and R_{2} respectively such that
R_{1} > R_{2}
- Draw a line joining the centres O and P.
- With centre O and radius equal to (R
_{1} + R_{2} ), draw a circle.
- From P , draw a line PT tangent to this circle.
- Draw a line OT cutting the circle at A.
- Through P , draw a line PB parallel to OA , on the other side of OP and cutting the circle at B.
- Draw a line through A and B. This is the required tangent.
- Similarly , draw another internal tangent through C and D.

Draw the given circles with centres O and P and radii R_{1} and R_{2} respectively such that
R_{1} > R_{2}
- Draw a line segment joining centres O and P.
- With centre O and radius (R
_{1} - R_{2} ) , draw a circle.
- From P , draw a tangent to the circle drawn in step 2.
- Draw a line through O and N to cut the outer circle at B.
- Through P , draw a line PD parallel to OB and cutting the circle with radius R
_{2} at D.
- Draw a line joining B and D , which is the required tangent.
- Similarly , draw another external tangent through E and F.

**A. External Tangents**
Draw the given circles with centres A and B
- Draw a line segment joining A and B
- At A and B construct perpendiculars to AB on its same side to intersect given circles at D and E.
- Draw a line joining D and E. This line is the required tangent. FG is the other tangent, which can be drawn similarly.

**B. Internal Tangents**
Draw the given circles with centres P and Q
- Draw a line segment joining P and Q.
- Bisect PQ at O. Draw a circle with OP as diameter to cut the circle at M and R.
- With centre O and radius OM , draw a circle to cut the other circle at S and N.
- Draw line through M and N. This is the required tangent.
- Similarly , draw a line through R and S , which is the other required tangent.