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 the external point from which the tangents \( PA \) and \( PB \) are drawn to the points of contact \( A \) and \( B \) on the circle.

2. **Understand the Tangent Properties**:
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