In a school garden a circular flower-bed of radius 5m is to be touched by a straight gravel path. A bench will be placed at a point P on the path such that the distance of the bench from the centre O of the flower-bed is 13m. Answer the following:
(i) Calculate the length of the tangent segment from P to the flower-bed.
(ii) Find the minimum distance of the bench from the centre so that the tangent segment is 14m.
(iii) Determine how far the bench must be shifted away from the centre compared to its original position.