NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 9: Circles - Exercise 9.2

Question 2

Step 1: Let the centre of the circle be O, radius = r (in SI units: metres, m).

Step 2: Take a point P outside the circle. The distance from the centre O to P is OP (in metres).

Step 3: The length of the tangent PT from point P is given by the formula:

\[ PT = \sqrt{OP^{2} - r^{2}} \]

Step 4: Suppose OP is only a little bigger than r. For example:

• If radius \(r = 10 \, \text{m}\),
• and distance \(OP = 10.1 \, \text{m}\),
• then tangent length \(PT = \sqrt{10.1^{2} - 10^{2}} = \sqrt{102.01 - 100} = \sqrt{2.01} \approx 1.42 \, \text{m}\).

Step 5: Here, the tangent length (≈ 1.42 m) is smaller than the radius (10 m).

Conclusion: The tangent length is not always greater than the radius. It can be smaller. Hence, the statement is False.