Question

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.

Step2: Identify radii

Segment $CB$ is a radius of the circle with center $C$. Segment $CD$ is also a radius of the circle with center $C$.

Answer:

Since $CB$ and $CD$ are both radii of the circle with center $C$, by the property that all radii of a circle are equal, the length of segment $CB$ is the same as the length of segment $CD$.