The chords AB and CD of the circle with center O are equal.

The chords AB and CD of the circle with center O are equal. Prove that two arcs with ends A and B, respectively, are equal to two arcs with ends C and D.

Consider triangles AOB and COD.

In the triangle ОАВ ОА = ОВ = R, and in the triangle СОD, OC = ОD = R, then ОА = ОВ = OC = ОD = R.

By condition, AB = CD, then the triangles AOB and COD are equal on three sides, and therefore the angle AOB = COD

Since the degree measures of the inscribed angles are equal, then the arcs on which they rest are also equal, then the arc AB is equal to the arc CD, which was required to prove.