It's easy to understand.

Suppose the mouse runs on a circle with radius r.

The cat is chasing on a circle with radius r.

There's always a way to make an alliance with cats.

The distance between them is R+r instead of r-R.

At this time, the mouse is only R-r from the shore.

The speed of a cat should be 3. 14R/(R-r) times that of a mouse.

The result must not be 3. 14.