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In given figure, from an external point \(P\), a tangent \(PT\) and a line segment \(PAB\) is drawn to a circle with centre \(O\). \(ON\) is perpendicular on the chord \(AB\). Prove that:
(i) \(PA \cdot PB = PN^2 - AN^2\)
(ii) \(PN^2 - AN^2 = OP^2 - OT^2\)
(iii) \(PA \cdot PB = PT^2\)
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