Theorem: In a circle, congruent chords subtend congruent arcs.

Arcs are congruent if they have the same measure and if they are on circles with the same radii.

Given congruent chords EF and CD, prove that arcs EF and CD are congruent.

For an additional hint, scroll down...

Construct auxiliary line segments AF, AE, AD and AC. Remember that the measure of arc EF equals the measure of central angle EAF.