[Puzzler] falling ladders

[Mike]

A ladder stands straight up against a wall. The ladder tips and falls to the floor while the base of it stays firmly in the corner.

Consider just the midpoint of the ladder. What path does it trace as it falls to the floor? This one's pretty simple. It makes a quarter circle.

Now picture the same ladder up against the wall. The bottom of the ladder slides out so that the top of the ladder slides down the wall. Eventually, the ladder is laying flat on the floor.

Now what path does the midpoint trace as the ladder drops to the floor?

Make your best guess, but then try to sketch it out. Or maybe just simulate it with a ruler and see what you think. My first guess was wrong, but the actual answer was pretty cool.

[Zen]

[Mike]

Zen, that was my first guess too.

[Tahlvin]

[Mike]

Tahlvin is correct!