from an external point P, a tangent PT and a secant PAB is
drawn to a circle with centre O. ON is perpendicular on the chord AB. Prove
(i) PA.PB = PN² – AN²
(ii) PN² – AN² = OP² – PT²
(iii) PA.PB = PT²
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Consider the following figure.P is an external point and PT is the tangent to the circle and AB is a chord to the circle. Thus, we have, ....(1)Consider the triangle ONA. ....(2) Consider the triangle OTP. From equations (1) and (3), we have,
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