Question

1. this diagram shows how 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. All radii of a circle are equal. Here, \(CD\) is a radius of the circle with center \(C\), and \(AB\) is used to set the radius of the circle, so \(AB\) is equal to the radius of the circle.

Step2: Analyze each option

• Option A: Since \(AB\) and \(CD\) are both radii of the circle, \(AB = CD\), so \(AB>CD\) is false.
• Option B: As \(AB\) is the length used to set the radius of the circle and \(CD\) is a radius of the circle, \(AB = CD\). This option is true.
• Option C: \(CE\) is a non - radius line segment. The radius of the circle is \(AB\) (or \(CD\)). \(AB\) is not greater than \(CE\) in the context of radius - setting. This option is false.
• Option D: \(CE\) is not a radius of the circle. \(AB\) is equal to the radius of the circle, so \(AB

eq CE\). This option is false.

Answer:

B. \(AB = CD\)