NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 10: Construction - Exercise 10.2
Question 3

Question. 3

A pair of tangents can be constructed from a point \(P\) to a circle of radius \(3.5\,\text{cm}\) situated at a distance of \(3\,\text{cm}\) from the centre.

Answer:

false

Detailed Answer with Explanation:

Step 1: Recall the condition for drawing a tangent from a point to a circle.

A tangent is possible only if the point lies outside the circle. This means the distance of the point from the centre (\(d\)) should be greater than or equal to the radius (\(r\)).

Step 2: Write the given values in SI units (cm).

  • Radius of circle, \(r = 3.5\,\text{cm}\)
  • Distance of point \(P\) from centre, \(d = 3.0\,\text{cm}\)

Step 3: Compare distance and radius.

Here, \(d = 3.0\,\text{cm}\) and \(r = 3.5\,\text{cm}\).

Since \(d < r\), the point \(P\) is inside the circle.

Step 4: Conclusion.

If the point is inside the circle, no tangent can be drawn. Therefore, the statement is false.

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 10: Construction – Exercise 10.2 | Detailed Answers