To draw a pair of tangents to a circle which are inclined to each other at an angle of `50^(@)`, it is required to draw tangents at the end points of there two radii of the circle, the angle between two radii is

Options

A. `105^(@)`
B. `130^(@)`
C. `75^(@)`
D. `125^(@)`

Answer

To find the angle between the two radii of a circle when the tangents at their endpoints are inclined to each other at an angle of \(50^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Geometry**:
- Let the center of the circle be \(O\).
- Let the points where the tangents touch the circle be \(A\) and \(B\).
- The angle between the tangents \(AB\) is given as \(50^\circ\).

2. **Identify the Angles**:
- The tangents at points \(A\) and \(B\) are perpendicular to the radii \(OA\) and \(OB\) respectively. Therefore, we have:
- \(\angle OAT = 90^\circ\) (where \(T\) is the point where the tangent touches the circle at \(A\))
- \(\angle OBT = 90^\circ\)

3. **Set Up the Equation**:
- The sum of the angles around point \(O\) is \(360^\circ\). We can express this as:
\[ \angle O + \angle OAT + \angle OBT + \angle AOB = 360^\circ \]
- Here, \(\angle OAT\) and \(\angle OBT\) are both \(90^\circ\), and the angle between the tangents \(AB\) is given as \(50^\circ\).

4. **Calculate the Angle \(AOB\)**:
- The angles around point \(O\) can be expressed as:
\[ \angle O + 90^\circ + 90^\circ + 50^\circ = 360^\circ \]
- Simplifying this gives:
\[ \angle O + 230^\circ = 360^\circ \]
- Therefore:
\[ \angle O = 360^\circ - 230^\circ = 130^\circ \]

5. **Conclusion**:
- The angle between the two radii \(OA\) and \(OB\) is \(130^\circ\).

### Final Answer:
The angle between the two radii of the circle is \(130^\circ\).