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Chords are equal, radii of a circle are equal tharefore in the 2 triangles that will be formed, chords will be equal
Radii will be equal
So by sss congurency the triangles and congruent
By cpct the angles are equal
Hence proved

Let us consider two circle of center C1 and C2, of radius r and R respectively two circle are congruent means there radius are equal,r=R join the chords with corresponding center.It will become a triangle,whose two side are of radius and other one is a chord by looking two circle simultaneously for C1 for C2 r = R r = R angle are same as given by SAS congruncy .two triangle are congruent Hence cord are equal by CPCT