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) The school authorities later decide that the tangent segment must be at least 14m. Find the minimum distance from the centre at which the bench should now be placed.
(iii) By how many metres must the bench be moved away from its original position to satisfy the new requirement?
b. (ii) Find the minimum distance of the bench from the centre so that the tangent segment is 14m.
c. (iii) Determine how far the bench must be shifted away from the centre compared to its original position.