Question : A tangent is drawn from a point M to a circle, which meets the circle at T such that MT = 12 cm. A secant MAB intersects the circle at points A and B. If MA = 8 cm, what is the length (in cm) of the chord AB?
Option 1: 16
Option 2: 10
Option 3: 12
Option 4: 9
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Correct Answer: 10
Solution : According to the concept, MA × MB = MT 2 ⇒ 8 × MB = 12 2 ⇒ MB = $\frac{144}{8}$ ⇒ MB = 18 ⇒ MA + AB = 18 ⇒ 8 + AB = 18 ⇒ AB = 18 – 8 ⇒ AB = 10 ∴ The measure of AB is 10 cm. Hence, the correct answer is 10.
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