Question

1. clare used a compass to make a circle with radius the same length as segment ab. she labeled the center c. which statement is true? a. ab > cd b. ab = cd c. ab > ce d. ab = ce

Explanation:

Step1: Recall circle - radius property

The radius of a circle is the distance from the center of the circle to any point on the circle. Here, the radius of the circle with center \(C\) is equal to the length of segment \(AB\) as per the construction. Also, \(CD\) is a radius of the circle with center \(C\) (since \(D\) is a point on the circle and \(C\) is the center).

Step2: Compare lengths

Since the radius of the circle is equal to \(AB\) and \(CD\) is a radius of the same circle, we have \(AB = CD\).

Answer:

B. \(AB = CD\)