In the diagram, \triangle A O B is a triangle with coordinates O=(0,0), A=(0,30), and B=(40,0). Let C be the point on A B for which O C is perpendicular to A B.
(a) Determine the length of O C.
(b) Determine the coordinates of point C.
(c) Let M be the centre of the circle passing through O, A, and B. Determine the length of C M.