Edit: It actually has to be inside of the circle made centered on one of the starting points and with the other starting point on the circle.
I'll give credit to OP's game however, giving you new tools once you have proved how to do something is great!
1) Use thicker lines, preferably in a color that contrasts better with white (although it'll be fine if the segment width is 2-4 pixels)
2) Support for drag + snap-to-intersect/vertex UX rather than click only. I instinctively tried this first.
3) Some sort of progress tracking (local storage or user accounts even perhaps)
Anyway, great idea and a promising start!
Great game, though. I'm on level 5 and having a lot of fun.
Thanks for your feedback!
 - http://sciencevsmagic.net/geo/
Minor UI feedback:
The undo button moves when you click it which is annoying if you intend to step back 2 or more steps.
It looks like Esc is the intended "nevermind" button, but it isn't obvious.
... because I'm stuck on #19
Anyway, I long for the day when someone writes a similar toy for a non-Euclidean plane.
The author could perhaps learn a bit about leveling from it, to make it more accessible to people trying to learn geometry (if that is the goal?)
I wanted to go through the Elements, but it wasn't clear how I could do it using a straight edge and compass. I couldn't find much guidance online.
One problem for me is that by default the comments from other users are shown, sometimes with the solution for the level.
You need to use the tools provided to create something that is guaranteed to be what is asked for.
For instance in the first level you aren't given a ruler, so you need to figure out how to do the level without using one.
I think that fits the requirements for a "fun game".
Also wouldn't a CAD program have bisect and what this calls compass2 from the get go?
Is it the norm this days to use CAD in technical drawing courses? Mine were strictly hand-drawn.