Question

Prove that equal chords of a circle substance equal angles at the centre

Answer 1

This is the answer of ypur question.

Answer 2

Theorem 1 - Equal chords of a Circle Subtend Equal Angles at the Centre. Theorem 1: Equal chords of a circle (or of congruent circles)subtend equal angles at the centre 

Given:  AB and CD are equal chords of the same circle with center as O.
To prove: angle AOB = angle COD

Proof:   In triangle AOB and triangle COD.
             AO = CO (radii of the same circle)
             AB = CD (given)
             OB = OC (radii of the same circle)

Therefore triangle AOB is congruent to triangle COD by SAS congruence rule..

This implies  angle AOB is equal to angle COD....
                                        Hence proved...