Turtle Spiral

Geometry Level 4

Four turtles sit on the vertices of a unit square (side length 1) as shown below.

At the same point in time, each turtle begins walking towards the turtle it is facing and continues to walk directly towards it. The turtles stop walking if they meet at a point. How far has each turtle travelled when they stop walking?

1.2 1.2 1 1 The turtles will never meet π 4 \frac\pi4

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