Question : The radius of a circle is 3 cm and 'O' is its centre. The length of the tangent (in cm) to the circle drawn from a point P, which is at a distance of 5 cm from 'O' is:
Option 1: 4
Option 2: 6
Option 3: 5
Option 4: 3
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Correct Answer: 4
Solution : Given: The radius of a circle OQ is 3 cm and 'O' is its centre. P at a distance of 5 cm from 'O'. If the tangent from P touches the circle at Q. Then, $\triangle$ PQO is a right-angled triangle and the length of the tangent is PQ. By using Pythagoras theorem, ⇒ OP 2 = PQ 2 + OQ 2 ⇒ 5 2 = PQ 2 + 3 2 ⇒ PQ 2 = 25 – 9 ⇒ PQ = 4 cm Hence, the correct answer is 4.
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