The angle between the tangents drawn from a point on the director circle `x^(2)+y^(2)=50` to the circle `x^(2)+y^(2)=25`, is

Answer

To solve the problem of finding the angle between the tangents drawn from a point on the director circle \(x^2 + y^2 = 50\) to the circle \(x^2 + y^2 = 25\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Circles**:
- The given circle is \(x^2 + y^2 = 25\), which has a radius \(r_1 = \sqrt{25} = 5\).
- The director circle for this circle is given by \(x^2 + y^2 = 50\), which has a radius \(r_2 = \sqrt{50} = 5\sqrt{2}\).

2. **Understanding the Director Circle**:
- The director circle of a given circle is a circle from which tangents drawn to the original circle will form right angles (90 degrees) with each other.

3. **Angle Between Tangents**:
- The angle between the tangents drawn from any point on the director circle to the original circle is always \(90^\circ\) or \(\frac{\pi}{2}\) radians.

4. **Conclusion**:
- Therefore, the angle between the tangents drawn from a point on the director circle \(x^2 + y^2 = 50\) to the circle \(x^2 + y^2 = 25\) is \(\frac{\pi}{2}\).

### Final Answer:
The angle between the tangents is \(\frac{\pi}{2}\) radians.