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 must be true? a. ab = cd b. ab = ce c. ab = cf d. ab = ef (from unit 1, lesson 1.)

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.

Step2: Identify given information

The radius of the circle is the same length as segment \(AB\). Let the circle have center \(C\). Then any line - segment from \(C\) to a point on the circle is a radius.

Step3: Analyze options

In a circle with center \(C\), if the radius of the circle is equal to the length of \(AB\), and \(CF\) is a radius (a line - segment from the center \(C\) to a point \(F\) on the circle), then \(AB = CF\).

Answer:

C. \(AB = CF\)