Final answer:
Triangle ABC is equilateral because AB = AC = BC.
Step-by-step explanation:
In order to prove that triangle ABC is equilateral, we need to show that all three sides are equal in length. Let's consider the two circles with centers A and B. Because both circles are equidistant from each other, the distance from A to B is the same as the distance from B to A. This means that AB = BA. Additionally, since A is the center of one circle and B is the center of the other, the radii of the circles are also equal in length, denoted as AC = BC. Now, we can see that AB = AC = BC, which means triangle ABC is equilateral.