Question : O is the centre of a circle with a diameter of 16 cm. Q is a point outside the circle and QS is tangent to the circle at point S. If OQ is =17 cm, what is the length (in cm) of the tangent QS?
Option 1: 15
Option 2: 12
Option 3: 18
Option 4: 10
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Correct Answer: 15
Solution : Given, Radius = 8 cm $O$ is the centre of the circle with $QS$ as a tangent. Also, $OQ$ = 17 cm Using Pythagoras theorem, $OQ^2=QS^2+OS^2$ ⇒ $17^2=8^2+QS^2$ ⇒ $QS$ = 15 cm Hence, the correct answer is 15.
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