Answer
The distance between B and A sets the length of overlap between the two circles, and the common chord AC prevents a change in the two circles' angular placements in relation to one another. Because these structures are in place - one involving angle, and one length - the congruence of the common chord and line segment of centers provides a right angle which establishes the structure of an equilateral square ABCD due to the length- and angle-similarities which occur as a result.
Work Step by Step
The problem asks for an explanation instead of a proof, so the reasoning is outlined above.
