Have you ever tried to move a large piece of furniture through a narrow hallway and found yourself stuck? Here we'll explore the classic problem: what is the longest ladder/piece of furniture that can make it around the corner in this hallway?
Controls

Use the sliders for a and b to adjust the widths of the hallways.

Drag point C to move the ladder through and see the longest possible ladder for that position.

Note: This is my first posting to GeoGebraTube.

Set a = 2 and b = 2. Slide point C to minimize the length of the ladder. What do you notice about the shape?

Set b = 4. Now slide C to minimize the length of the ladder. What has changed?

Try to generalize the relationship between a & b and the location of C.

Challenge: How could you extend this simulation to three dimensions?