Question

An observer stands at a point P, one unit away from a track. Two runners start at the point S in the figure and run along the track. One runner runs 2 times as fast as the other. Find the maximum value of the observer's angle of sight è between the runners.
Thank you so much!

Answer 1

well, naturally, the maximum angle will be when the two runners are at opposite ends of a diameter perpendicular to the line from the observer to the center of the circle.

If the track has radius r, then

max θ = 2arctan(r)

For lack of a diagram, I am unable to incorporate any further constraints.