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A circle with radius 4410001/2 is drawn at on a Cartesian plane with the origin as its centre.
How many lattice points (coordinate with integer coordinates) does it pass?
Train X moves at an uniform speed from Powersdale to Quicksville; two stations 240 kilometers apart. Train Y starts from Powersdale precisely one hour after Train X departed (also from Powersdale) and, after two hours, comes to a point that Train X had passed 45 minutes previously.
Train Y now increases its speed by 5 kilometers per hour and it overtakes Train X as soon it reaches Quicksville.
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