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?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 8.75.
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 of the chord AB is 8.75 cm