Question

Write the proof of the theorem "Equal chords of a circle subtend equal angles at the center"

Answer 1

Answer:

Theorem 10.1 Equal chords of a circle subtend equal angles at the center. ... CD are equal chords of circle i.e. AB = CD To Prove : ∠AOB = ∠DOC Proof : In ΔAOB & ΔDOC AO = OD ...

Answer 2

Step-by-step explanation:

Given: (Image is attached with the answer) A circle with center O.

           AB and CD are equal chords of circle. i.e. AB=CD

To prove: ∠AOB = ∠DOC

Proof: In ΔAOB and ΔDOC

          AO=OD (Radius)

          AB=CD (Given)

         OB=OC (Radius)

∴ ΔAOB ≅ ΔDOC (SSS rule)

∴  ∠AOB = ∠DOC (CPCT rule)

Hence, Proved.

I hope you got your answer.