TITLE: How to make a perpendicular construction in 3 moves?
QUESTION [25 upvotes]: I've been playing Euclid: The Game for some time now. I'm quite addicited to it, trying to get all the records now. Suprisingly, I'm not able to get a record for some really early level. In Level 4 (http://euclidthegame.com/Level4/), I'm trying to get the record for primitive tools. Primitive tools means that you can only use the first 5 tools (compass and straigthedge), and not any tool that you unlock in later levels.
The current record is 3 moves, but I really don't get how that could be possible. The best I can do is 4 moves. 


Create a random point on the line B
Create a circle with center A and radius AB.
Create a point at the intersection of the line and the circle
Create a circle with center C and radius BC
Create a circle with center B and radius BC
Create a point at the intersection of the circles (D)
Craete the segment AD.

Point creation is not counted as a move, so this is 4 moves, but how can you do this possibly in 3 moves ?
Oh, one more thing, the goal of this level is: Construct a line (segment) that goes through point A and that is perpendicular to the given line segment.

REPLY [5 votes]: Solution


Create a random point $B$ outside the line, and make a circle from $B$ to $A$.
Let the other intersection of the circle and the line be $C$, make a line from $C$ to $B$, which intersects the circle at $D$.
Make the line $AD$. It will be the perpendicular line.