Question

prove that the equal chords ab and CD of a circle subtend equal angles at the centre use the above to find angle abc in figure 4 where O is the centre of the circle ​

Answer 1

The equal chords AB and CD of a circle subtend equal angles ∠AOB and ∠COD at the center of O of the circle.

• Given,
• AB and CD are the equal chords of a circle.
• O is the center of the circle.
• From given figure, consider,
• ΔAOB and ΔCOD
• we have,
• OA=OC
• OB=OD
• AB=CD
• From SSS theorem, we have,
• ΔAOB≅ΔCOD
• Hence, from congruence parts of congruent triangle, we get,
• ∠AOB=∠COD