Question

if square abcd is inscribed in the circle, which of the following statements is true about $overline{cd}$?
it is perpendicular to $overline{bd}$.
it is perpendicular to $overline{ab}$.
its length is equal to the side of the square.
its length is equal to the radius of the circle

Explanation:

Step1: Recall properties of a square

In a square \(ABCD\), all sides are equal. That is, \(AB = BC=CD = DA\).

Step2: Analyze perpendicular - side relationships

In a square, adjacent sides are perpendicular. So \(CD\perp AD\) and \(CD\perp BC\), and \(CD\) is parallel to \(AB\). Also, the diagonals of a square are not perpendicular to the sides in the way described in the first option. And the side - length of a square inscribed in a circle is not equal to the radius of the circle.

Answer:

C. Its length is equal to the side of the square.