 Hi and how are you all today? My name is Priyanka. The question to be discussed is prove that if chords of congruent circles subtend equal angle at their centers, then the chords are equal. So what we need to do over here is first of all write down whatever is given to us in the question. We are given that circles with center, the figure to be referred is this. The circles with center O congruent that is their radius that is O A is equal to O B is equal to C M is equal to M D. The radius of these congruent circles are given that the angles that they are subtending at the center are angle A O B is equal to angle C M D. This is also given to us in the question. What we need to prove is we need to prove A B is equal to our proof. As we know congruent triangles have equal radius, congruent circles over here is congruent circles radii. This is given to us in the question. Then we are also given that angle A O B is equal to angle C M D. It is given to us in the question and again O B is equal to M D again with the same reason that congruent circles radii. So all the radius are equal to each other. So by S congruency rule we can say that therefore triangle A O B is congruent to triangle C M D by congruency rule. Say that therefore A B is equal to C D. C D that is congruent part of congruent triangle. These are congruent triangles we have proved over here. So all the congruent parts of these congruent triangles will also be equal to each other. So this completes our proof. Hope you enjoyed the session. Take care and bye for now.