Question : A tangent AB at point A of a circle of radius 6 cm meets a line through the centre O at point B. If OB = 10 cm, then the length of AB (in cm) is equal to:
Option 1: 5
Option 2: 6
Option 3: 4
Option 4: 8
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Correct Answer: 8
Solution : Given, AB is a tangent, OB = 10 cm and OA = 6 cm Since tangent is perpendicular to the radius at its point of contact, $\angle$OAB = 90$^\circ$ Using Pythagoras theorem, OB 2 = AB 2 + OA 2 ⇒ 10 2 = AB 2 + 6 2 ⇒ AB 2 = 64 ⇒ AB = 8 cm Hence, the correct answer is 8.
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