Show that the marked triangle is equilateral



Since \(B\) and \(C\) lie on a circle with center \(A\), their distance from \(A\) is the same.
This shows that 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 three triangle sides have the same length.