Let O be the centre of a circle and P be the point outside the circle. If PAB is a secant to the circle intersecting the circle at A and B and PT is the tangent segment drawn from P, find the length of PT, if PA = 3 cm and AB = 9 cm.

$3\sqrt{3}$ cm $4\sqrt{3}$ cm 6 cm 8 cm

6 cm

According to the concept PA x PB = \( { PT}^{2 } \) ⇒ 3 x (3 + 9) = \( { PT}^{2 } \) ⇒ \( { PT}^{2 } \) = 36 ⇒ PT = 6 Therefore, PT is 6 cm.