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A quadrilateral ABCD is drawn to circums...

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that `A B+C D=A D+B C`

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To prove that in a quadrilateral ABCD that circumscribes a circle, the equation \( AB + CD = AD + BC \) holds true, we can follow these steps: ### Step 1: Understand the Properties of Tangents When a circle is inscribed in a quadrilateral, the points where the circle touches the sides of the quadrilateral are important. Let’s denote the points of tangency as follows: - The circle touches side \( AB \) at point \( P \) - The circle touches side \( BC \) at point \( Q \) - The circle touches side \( CD \) at point \( R \) - The circle touches side \( DA \) at point \( S \) ...
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