In the figure both circles are congruence because radius AB=radius AC of one circle and radius AB = radius BC of the other circle ( radii of circles are same ). Therefore line segment AB = line segment BC= line segment AC but these are the sides of the triangle ABC. So Δ ABC is an equilateral triangle .
But we know that an equilateral Δ has three equal angles and we say that ∠ABC=∠BCA. Hence we can use the reason A, to prove the ∠ABC =∠BCA.