In \\( \ riangle \\mathrm{AOB}\\) and \\( \ riangle \\mathrm{CO'D}\\)
\\( \\angle A O B=\\angle C O^{\\prime} D\\) (given)
OB = O'D (Chords of same length)
OA = O'C (Radii of congruent circles)
\\( \ riangle \\mathrm{AOB}\\) \\( \ riangle \\mathrm{CO'D}\\) (SSS congruence rule)
AB=CD (By CPCT)
Hence , if the chord of congruent circle equal angles at their centers, then the chords are equals.