Two opposite points on the rim of a circular park have coordinates G(3,7) and H(11,−1) in metres with respect to a chosen origin.
(i) Find the centre and radius of the park.
(ii) Write the equation of the boundary of the park in general form.
(iii) Determine whether the origin lies inside, on, or outside the park. Justify your answer with suitable calculations.
(iv) Calculate the length of fencing required to be laid along the boundary of the park (take π as a symbol).