If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices ofthe quadrilateral, prove that it is a rectangle

Explanation

To prove that a cyclic quadrilateral with diagonals that are diameters of the circle is a rectangle, we will follow these steps:

### Step 1: Understand the given information
We have a cyclic quadrilateral \(ABCD\) inscribed in a circle, where the diagonals \(AC\) and \(BD\) are diameters of the circle.

### Step 2: Identify the center of the circle
Let \(O\) be the center of the circle. Since \(AC\) and \(BD\) are diameters, points \(A\), \(C\), \(B\), and \(D\) lie on the circumference of the circle.

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