If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.

Explanation

To prove that the two chords AB and CD are parallel given that the line segment joining their mid-points G and H passes through the center O of the circle, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Chords and Mid-Points**:
Let AB and CD be two chords of the circle, with G as the mid-point of chord AB and H as the mid-point of chord CD.

2. **Draw the Line Segment**:
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