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
135°
90°
60°
120°
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)