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?

10

According to the concept,

MA x MB = \( {MT }^{2 } \)

⇒ 8 x MB = \( {12}^{2 } \)

⇒ MB = \(\frac{144}{8}\)

⇒ MB = 18

⇒ MA + AB = 18

⇒ 8 + AB = 18

⇒ AB = 18 - 8

⇒ AB = 10

Therefore, the measure of AB is 10 cm.