Question

points a and b are each at the centers of circles of radius ab. 1. compare the distance ea to the distance eb. be prepared to explain your reasoning.

Explanation:

Step1: Recall circle - radius property

Since point \(A\) is the center of a circle and \(E\) lies on the circle centered at \(A\), by the definition of a circle, \(EA\) is the radius of the circle centered at \(A\), so \(EA = AB\).

Step2: Recall circle - radius property for the other circle

Since point \(B\) is the center of a circle and \(E\) lies on the circle centered at \(B\), by the definition of a circle, \(EB\) is the radius of the circle centered at \(B\), so \(EB=AB\).

Step3: Compare \(EA\) and \(EB\)

Since \(EA = AB\) and \(EB = AB\), we can conclude that \(EA=EB\).

Answer:

The distance \(EA\) is equal to the distance \(EB\).