NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 10: Construction - Exercise 10.1
Question 6

Question.  6

To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

(A)

135°

(B)

90°

(C)

60°

(D)

120°

Detailed Answer with Explanation:

Step 1: Recall that the angle between two tangents drawn from an external point is related to the angle between the radii drawn to the points of contact.

Step 2: The radius of a circle is always at right angles (90°) to the tangent at the point of contact.

Step 3: So, when we connect the centre of the circle to the points where tangents touch, we get an isosceles triangle (two equal radii).

Step 4: In that triangle, the angle at the external point (between the tangents) and the angle at the centre (between the radii) are supplementary (they add up to 180°).

Step 5: Here, the angle between the tangents = 60°.

Step 6: Therefore, the angle between the radii = 180° − 60° = 120°.

Final Answer: 120° (Option D)

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 10: Construction – Exercise 10.1 | Detailed Answers