Statement:
''If two circles are drawn with centres at points \(A\) and \(B\) of a line segment \(AB\), each having a radius equal to \(AB\), then the points of intersection of the circles form symmetric triangles with \(AB\) as the base."
Analyse the above statement geometrically and answer the following questions.
Interpretation:
(i) Is the statement true?
(ii) If yes, at how many points does the circle intersect?
(iii) How many symmetric triangles can be formed using the points of intersection of the circles and the centres \(A\) and \(B\)?