Question

prove that if 2 chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Answer 1

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

Answer 2

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