I drew a line through the center points of the circles and perpendiculars to that line through the centers. I then marked the points where the perpendicular lines crossed the circles. These are A,B,C and D.

I drew a line through A and B and marked the point E where it crossed the line through the centers of the circles. I knew this point would be on the two tangent lines I wanted.

I then constructed a segment from E to the center of the smaller circle and found its midpoint F. I hid the line through A and B because it was not needed anymore.

I then constructed a circle with center F and with segment FE as a radius and marked the points, G and H, where this circle crossed the smaller circle. I hid lines AC and BD because they were not needed anymore.

I constructed lines EG and EH which were the two tangent lines I was looking for.

I then hid all of the other construction lines and I was done.