- Colin Beveridge
Level 20 of http://euclidthegame.org/Level20.html asks you to construct the outer tangent to two given circles (here, a, with centre A; and b, with centre B). Here's how I'd do it.
Draw a radius of circle b (BF) and a parallel radius of circle a (AG). Draw lines AB and GF; these intersect at point H. Construct a circle through H and B, which intersects circle b at T. HT is tangent to both circle a and circle b.