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

The distance from the center of a circle to any point on the circle is equal to the radius of the circle.

Step2: Identify radii in the circles

In the circle with center \(A\), \(EA\) is a radius since \(E\) lies on the circle centered at \(A\). In the circle with center \(B\), \(EB\) is a radius since \(E\) lies on the circle centered at \(B\). And we are given that the radii of the two circles are equal (\(AB\) is the radius of both circles as the circles are constructed with equal - radius condition).

Answer:

The distance \(EA\) is equal to the distance \(EB\) because \(EA\) and \(EB\) are radii of circles with equal radii.