UPSKILL MATH PLUS

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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) \(PA \cdot PB = PT^2\)
 
YCIND_240308_6083_circles_9.png
 
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Important!
This is a self assessment task. Solve this question and assess the solution steps after the completion of test on your own.