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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