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Prove that opposite sides of a quadrilat...

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

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To prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle, we will follow these steps: ### Step-by-Step Solution: 1. **Understanding the Configuration**: Let \( ABCD \) be a quadrilateral that circumscribes a circle with center \( O \). The points where the circle touches the sides \( AB, BC, CD, \) and \( DA \) are denoted as \( P, Q, R, \) and \( S \) respectively. 2. **Identifying Tangents**: ...
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