Question : Find the length of a tangent drawn to a circle with a radius of 6 cm, from a point 10 cm from the centre of the circle.
Option 1: 12 cm
Option 2: 9 cm
Option 3: 8 cm
Option 4: 10 cm
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Correct Answer: 8 cm
Solution :
Given: a circle with a radius $OQ$ = 6 cm
$OP$ = 10 cm
By using Pythagoras theorem,
⇒ $OP^{2} = PQ^{2}+OQ^{2}$
⇒ $10^{2} = PQ^{2}+6^{2}$
⇒ $PQ^{2}=64$
⇒ $PQ=8$
So, the length of the tangent is 8 cm.
Hence, the correct answer is 8 cm.
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