Question

1. here is a diagram of a straightedge and compass construction. c is the center of one circle, and b is the center of the other. explain why the length of segment cb is the same as the length of segment cd. (from unit 1, lesson 3.) (from unit 1, lesson 1.)

Explanation:

Step1: Recall circle - radius property

In a circle, all radii are equal. Point \(C\) is the center of one circle. Segments \(CB\) and \(CD\) are both radii of the circle with center \(C\).

Answer:

Since \(CB\) and \(CD\) are radii of the same circle (the circle with center \(C\)), by the property that all radii of a circle have the same length, the length of segment \(CB\) is the same as the length of segment \(CD\).