Show that the marked triangle is equilateral



Since \(B\) and \(C\) lie on a circle with center \(A\), the segments \(AB\) and \(AC\) have the same length.
Reasoning analogously exchanging the roles of \(A\) and \(B\), the segments \(AB\) and \(BC\) have the same length.
Thus the triangle \(ABC\) is equilateral.