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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