A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB+CD=AD+BC.
or
A circle touches all the four sides of a quadrilateral ABCD. Prove that AB+CD=BC+DA.

Explanation

To prove that in a quadrilateral ABCD that circumscribes a circle, the relation \( AB + CD = AD + BC \) holds, we can follow these steps:

### Step 1: Understand the properties of tangents
When a circle is inscribed in a quadrilateral, the tangents drawn from any external point to the circle are equal in length. This means that if we take any vertex of the quadrilateral, the lengths of the tangents from that vertex to the points where the circle touches the sides of the quadrilateral will be equal.

### Step 2: Assign tangent lengths
Let:
- \( AP \) and \( AS \) be the lengths of the tangents from point A to the points where the circle touches sides AB and AD respectively.
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