Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

Explanation

To prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the center, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Elements**:
Let \( O \) be the center of the circle, \( P \) be an external point from which two tangents \( PA \) and \( PB \) are drawn to the circle, touching the circle at points \( A \) and \( B \) respectively.

2. **Define the Angles**:
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