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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