Question

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 the property of radius

The radius of a circle is the distance from the center of the circle to any point on the circle. Here, \(CD\) is the radius of the circle with center \(C\). Since Clare made a circle with radius the same length as segment \(AB\), \(AB\) is also a radius.

Step2: Compare the lengths

Since \(AB\) and \(CD\) are both radii of the circle (by construction), \(AB = CD\). For \(CE\), \(CE=CF + FE\) and \(CF\) is a radius (\(CF = AB = CD\)), so \(CE>CF\) (because \(FE>0\)), which means \(CE>AB\).

Answer:

B. \(AB = CD\)