Here is the complete picture showing the scale and the positions of the circles, including the largest green circle of radius 10cm. The centres of the red and blue circles are 20cm apart.
The large green circle has its centre midway between the other two and it cuts them at the point of their tangents. So it's easy to draw the tangents. The green circle can then be erased just leaving the tangents accurately placed. You'll need a large sheet of paper (at least 33cm wide) if you draw the picture to actual size (the circle radii are 5cm and 8cm). The size of A3 paper is roughly 30cm by 42cm and would be suitable for your drawing.
Yes, you only need compasses and a straight edge, and, ideally, graph paper. And, yes, use the title BIFOCALS by all means.