Circles

In 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 . PB  =  PN²  – AN²

(ii) PN²  – AN²  =  OP²  –  OT²

(iii) PA.PB  =  PT²