I love this, exactly what I want from this kind of game.
I found a solution what I'm pretty sure correct (altough take many more step than what the game expect) and the game don't accept it:
No idea how to write spoiler so I just put a bunch of space here:
When have to make an equilateral triangle inside a circle, my logic was to draw a line from the center, then construct a 30 degree angle where that line meet with the circle, then where the new line meet with the circle, construct a 60 degree line, then connect where it meet with the circle to the first point. So all angle should be 60 degree, but the game don't like it :C