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A tangent is drawn from a point P to a circle, which meets the circle at T such that PT = 8 cm. A secant PAB intersects the circle in points A and B. If PA = 5 cm, what is the length (in cm) of the chord AB?

A tangent is drawn from a point P to a circle, which meets the circle at T such that PT = 8 cm. A secant PAB intersects the circle in points A and B. If PA = 5 cm, what is the length (in cm) of the chord AB? Correct Answer 7.8

Given:

PT = 8 cm

PA = 5 cm

Concept used:

Tangent secant theorem

PT2 = PA × PB

Calculation:

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We know that,

PT2 = PA × PB

⇒ (8)2 = 5 × PB

⇒ 64 = 5PB

⇒ PB = (64/5)

⇒ PB = 12.8 cm

Then,

AB = (12.8 – 5) = 7.8 cm

∴ The length of chord AB is 7.8 cm 

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