Stuck at lvl 20
Hint, although there is a faster solution in the comments in that site:
Some judicious use of Thales/similitudes should help you find out where the outer tangents intersect each other, and then you just have to draw the tangent to the circle through that point. The same applies for the inner tangents, although the picture does get more crowded.
20 is the last level. I found 11 (or was it 13? The one where you have to trisect a distance) and 19 interesting too
Inb4 Ozle posts more cryptic puzzles.
I'll correct my previous post: level 11, where you have to move an angle around, was interesting. Didn't find any pretty way to do it, though, just translated the two segments and then drew a bunch of circles and perpendicular lines. EDIT: ok, no, found a way cleaner way to do it. Circles are cool.
I think I did 19 as Walrus,
radius of circumscribed circle of equilateral triangle is 1/sqrt(3) of side, rinse and repeat. Was a complete mess by the end
eHalcyon's solution is much prettier! I did encounter the same bug he did, the segment AB didn't want to intersect with my other stuff, so I had to draw extra lines.