Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Explanation

To prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle, we can follow these steps:

### Step 1: Understand the Setup
Let \(ABCD\) be a quadrilateral that circumscribes a circle with center \(O\). The sides \(AB\), \(BC\), \(CD\), and \(DA\) are tangent to the circle at points \(P\), \(Q\), \(R\), and \(S\) respectively.

### Step 2: Draw Radii and Tangents
Draw the radii from the center \(O\) to the points of tangency:
- \(OP\) is perpendicular to \(AB\)
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