Suppose that A, B, and C are 3 points in a plane, such that AB = AC = BC = 1. At each point in time, A is moving toward B, B is moving toward C, and C is moving toward A, all with speed v = 50.

This is what the movement will look like. The red curve represents the path of point A, the green curve - the path of point B, the blue curve - the path of point C.

At what time(t)  will all the points be the same point? Express your answer to the third decimal place.