The range of values of `lambda,(lambda>0)` such that the angle `theta` between the pair of tangents drawn from `(lambda,0)` to the circle `x^2+y^2=4` lies in `(pi/2,(2pi)/3)` is (a) `(4/(sqrt(3)),2/(sqrt(2)))` (b) `(0,sqrt(2))` (c) `(1,2)` (d) none of these

Explanation

To solve the problem, we need to find the range of values of \( \lambda \) (where \( \lambda > 0 \)) such that the angle \( \theta \) between the pair of tangents drawn from the point \( (\lambda, 0) \) to the circle \( x^2 + y^2 = 4 \) lies in the interval \( \left( \frac{\pi}{2}, \frac{2\pi}{3} \right) \).

### Step-by-Step Solution:

1. **Identify the Circle and Point**:
- The equation of the circle is \( x^2 + y^2 = 4 \), which has a center at the origin \( (0, 0) \) and a radius \( r = 2 \).
- The point from which the tangents are drawn is \( (\lambda, 0) \).

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