Because the point A is the center of the circle BCD, Definition 11 tells us that AC is equal to AB. next Because the point B is the center of the circle ACE, BC is equal to AB. next But CA is equal to AB and things that are equal to the same thing are equal to each other by Axiom 1, therefore CA is equal to CB. next Now, since CA, AB, and CB are all equal to one another, triangle ABC must be equilateral.