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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


Team Careers360 3rd Jan, 2024
Answer (1)
Team Careers360 21st Jan, 2024

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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