How to make a perpendicular construction in 3 moves?

I'm the developer of Euclid: The Game. I'm glad you like the game, don't worry about that you can't get this solution in 3 moves.

Only very recently this record is set. No-one in the top 10 of the highscores has been able to do this, in fact, from all the scores that are submitted, no-one has ever done this in 3 moves.

Some user noted in the comments that it was possible in 3 moves, well I didn't believe it, but he showed me his solution, and it is actually quite simple (but that is true for a lot of things in mathematics).

I'm not going to give the solution here, I'm sure one time someone will spoil it in the comments, and maybe you get an answer here, that is fine with me as well, but I don't want to be responsible for spoiling my own game !

Well, I could give a hint. Your first move shouldn't be to create a random point on the line.

Hint:

If you draw three points on a circle in a certain way, you get a right angle.

Name of the theorem helpful for this solution:

Thales' theorem

From wikipedia:

if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle