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

Options

A. `135^(@)`
B. `90^(@)`
C. `60^(@)`
D. `120^(@)`

Explanation

To solve the problem of drawing a pair of tangents to a circle that are inclined to each other at an angle of \(60^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Draw the Circle**: Begin by drawing a circle with a center \(O\).

2. **Draw the Radii**: From the center \(O\), draw two radii \(OA\) and \(OB\) such that the angle between them is \(60^\circ\). This means that \(\angle AOB = 60^\circ\).

3. **Draw the Tangents**: At points \(A\) and \(B\) (the endpoints of the radii), draw the tangents \(AC\) and \(BD\) to the circle. By the properties of tangents, we know that the radius at the point of contact is perpendicular to the tangent line.

4. **Identify Angles**: Since \(OA\) and \(OB\) are radii, we have:
- \(\angle OAC = 90^\circ\) (tangent at point \(A\))
- \(\angle OBD = 90^\circ\) (tangent at point \(B\))

5. **Consider the Quadrilateral**: Now, consider the quadrilateral \(OABC\):
- The sum of the angles in a quadrilateral is \(360^\circ\).
- Thus, we can write the equation:
\[ \angle ABC + \angle BOC + \angle COA + \angle OAB = 360^\circ \]

6. **Substituting Known Angles**: We know:
- \(\angle OAB = 90^\circ\)
- \(\angle OBA = 90^\circ\)
- \(\angle ABC = 60^\circ\)
- Therefore, we can substitute these values into the equation:
\[ 60^\circ + \angle BOC + 90^\circ + 90^\circ = 360^\circ \]

7. **Solve for \(\angle BOC\)**: Simplifying the equation:
\[ 60^\circ + \angle BOC + 180^\circ = 360^\circ \]
\[ \angle BOC = 360^\circ - 240^\circ = 120^\circ \]

8. **Conclusion**: The angle between the two radii \(OA\) and \(OB\) is \(120^\circ\).

### Final Answer:
The angle between the two radii should be \(120^\circ\).

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