The figure <em>looks</em> symmetrical, but their is no given information indicating it actually <em>is</em> symmetrical. Thus we can't make any statements about the segment lengths. Nor is there any indication that any of the arc lengths are identical.
If we rule out statements about segments and arcs, that only leaves statements about angles. As it happens both of those are true: inscribed angles that intercept the same arc are congruent.
