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 ?
Answer & explanation
Correct answer: option 2
Let AB = x cm
By tangent secant theorem, \( {PT }^{2 } \) = PA x PB
⇒ \( {10.5 }^{2 } \) = 7 x PB
⇒ 110.25 = 7 x PB
⇒ PB = \(\frac{110.25}{7}\) = 15.75 cm
⇒ Here, AB = PB - PA
⇒ x = 15.75 - 7 = 8.75 cm
Therefore, the length of the chord AB is 8.75 cm.