Question

Here is a diagram of a straightedge and compassconstruction. C is the center of one circle, and B is the centerof the other. Explain why the length of segment CB is thesame as the length of segment CD.

Answer 1

It is stated that segment CB, which goes from the center of the bigger circle to the center of the smaller, has the same length of the segment CD.

Note that the center of the shorter circle (point B) is right in the perimeter (the circumference) of the bigger circle. The same for point D. It is right in the perimeter of the bigger circle.

Following the definition of circumference, it is a series of points that have exactly the same distance to the cener of it (ponint C). Then, any pair of points of the circumference (as are B and D) have the same distance to C, being the radius of the circumference.

Then, recalling the definition of circumference, we can say that length CB is equal to lenght CD, since C is the center of the circumference, and B and D are located in the perimeter of it.