Question

proved that equal chords of a circle subtend equal angel at the centre.

Answer 1

In the above diagram, we have: 
A circle with center O 
PQ and RS are the chords of Circle 
Angle subtended by chord PQ at the center of circle is ∠ POQ 
Angle subtended by chord RS at the center of circle is ∠ ROS 

And we need to prove that: 
∠ POQ = ∠ ROS 

In the above diagram, we have two Triangles (as highlighted below): 
△ PQO = △ RQO 



OP = OR (radii of circle are always equal) 
OQ = OS (radii of circle are always equal) 
PQ = RS (equal chords of circle - Given) 
Therefore, on applying SSS Rules of congruency, we get: 
∆ PQO ≅ ∆ RQO 

Since, we know that corresponding parts of congruent triangles are equal, so we get: 
∠ POQ = ∠ ROS