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Because it's a chord not a diameter.
Yes but a chord cannot be bigger than the circle's diameter which is its largest chord.
You cannot. If you rotate the circle around its centre, the lengths of the radius and chord will remain the same but the coordinates of the chord will change.
Different pools have different proportions.
Unless the chord is the diameter, there is no way to measure the radius of the circle. This is because the radius is in no way dependent on chord length since circles have infinite amount of chord lengths.