Two parallel chords of a circle of radius 2 units are `(sqrt3+1)` units apart. If these chords subtend, at the centre, angles of `90^@ /k" and "180^@/k`, where kgt0, then find the value of k.

Explanation

To solve the problem, we need to find the value of \( k \) given two parallel chords of a circle with radius 2 units that are \( \sqrt{3} + 1 \) units apart. The chords subtend angles of \( \frac{90^\circ}{k} \) and \( \frac{180^\circ}{k} \) at the center of the circle.

### Step-by-Step Solution:

1. **Understanding the Geometry**:
- Let the center of the circle be \( O \).
- Let the two parallel chords be \( AB \) and \( CD \).
- The distance between the two chords \( AB \) and \( CD \) is given as \( \sqrt{3} + 1 \).
...