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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