Two concentric circles with common centre O have radii 9 cm and 15 cm. From an external point P, tangents are drawn to both circles, touching the smaller circle at A and the larger circle at C. The length PC is 20 cm.
(i) Show that OP = 25 cm.
(ii) Hence, find the length of PA.
(iii) Prove that triangle OPC is right-angled at C.