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A tangent is drawn from a point P to a circle, which meets the circle at T such that PT = 10.5 cm. A secant PAB intersects the circle in points A and B. If PA = 7 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 = 10.5 cm. A secant PAB intersects the circle in points A and B. If PA = 7 cm, what is the length (in cm) of the chord AB? Correct Answer 8.75

Given:

PT = 10.5 cm

PA = 7 cm

Concept used:

Tangent secant theorem: When a tangent and secant segment are drawn to a circle from an exterior point, the square of the tangent segment's measure equals the product of the secant segment's and its external secant segment's measurements.

Calculation:

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Let, AB = x cm

By tangent secant theroem, PT2 = PA × PB

⇒ (10.5)2 = 7 × PB

⇒ 110.25 = 7 × PB

⇒ PB = 110.25/7 = 15.75 cm

Here, AB = PB - PA

⇒ x = 15.75 - 7 = 8.75 cm

∴ The length (in cm) of the chord AB is 8.75 cm

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