A Determined Cat on a Ladder!

A ladder is leaning against a wall. On the center rung is a cat. She must be a very determined cat, because she remains on that rung as we draw the foot of the ladder away from the tree until the ladder is lying flat on the ground. What path does the cat describe as she undergoes this indignity?

She follows this path!

A Path Followed by Determined Cat

What was the question?

 Interestingly, the cat follows the circular path whose center is at the foot of tree. 

Actually, as ladder is drawn out a series of right triangles with the same hypotenuse (the ladder) are created with respect to the foot of tree.

The point of hypotenuses where cat is sitting determinedly will be always at the same distance from all 3 vertices. So if all such point are joined then we get a circular path having center at the foot of tree. 

(Figure is for illustration purpose only & may not have accurate measurements.