Question

The diagram is a straightedge and compass construction. A is the center of one circle, and B is the center of the other.

Explain why segments AC, CB, BD, and AD are all the same length.

Answer 1

You could use Pythagoras Theorem to solve this.

All the points are equidistant from the centre of line AB, therefore it is just the same triangle but rotated. I hope this help but I can show you on paper if you don’t understand that answer :)

Answer 2

All the segments AC, CB, BD, and AD are same in length because all are radiuses of the circles which have same dimensions.

What is a radius?

Radius is the distance between circle center point and the point at its circumference.

In the given problem,

AC and AD are clearly the radiuses of the circle whose center is at point A (say first circle). Therefore these must be equal in length.

AC = AD

Similarly, BC and BD are the radiuses of the circle whose center is at point B (say second circle) . Therefore these are also equal in length.

BC = BD

Now you can observe that the first circle has a radius AB also which is equal to the radius of second circle i.e., BA.

∴ Both the circles has same radius length.

and

∴AC = AD = CB = BD

Hence all the segments which are nothing but the radiuses of both the circles must be equal.

To learn more about radius, refer to the link:

https://brainly.com/question/13449316

#SPJ2