Question : Let O be the centre of the circle and P be a point outside the circle. If PAB is a secant of the circle which cuts the circle at A and B and PT is the tangent drawn from P, then find the length of PT, if PA = 3 cm and AB = 9 cm.
Option 1: $3 \sqrt{3} \mathrm{~cm}$
Option 2: $4 \sqrt{3} \mathrm{~cm}$
Option 3: 6 cm
Option 4: 8 cm
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Correct Answer: 6 cm
Solution :
Let O be the centre of a circle. PAB is a secant of the circle.
PA = 3 cm and AB = 9 cm
If PAB and PT are a secant and a tangent respectively drawn from external point P, then PA × PB = PT
2
⇒ 3 × (9 + 3) = PT
2
⇒ PT = 6 cm
Hence, the correct answer is 6 cm.
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