Prove that the parallelogram circumscribing a circle is a rhombus.

Explanation

To prove that a parallelogram circumscribing a circle is a rhombus, we will follow a step-by-step approach.

### Step 1: Define the Parallelogram
Let \(ABCD\) be a parallelogram that circumscribes a circle. The points where the circle touches the sides of the parallelogram are denoted as \(P, Q, R, S\) on sides \(AB, BC, CD, DA\) respectively.

### Step 2: Use the Tangent Properties
According to the properties of tangents from an external point to a circle, the lengths of the tangents drawn from a point outside the circle to the points of tangency are equal. Therefore, we have:
- \(AP = AS\)
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