Question

(98 points) Prove that equal chords subtend equal angles at the centre.

Answer 1

Hey mate here is your answer

Answer:

consider a circle with centre O and two equal chords AB and CD. the radii to the ends of the chords are OA, OB and OC, OD respectively.

in ∆OAB and ∆OCD:

(i) OA = OC

(ii) OB = OD

(iii) AB = CD

therefore ∆OAB congruent to ∆OCD

therefore <AOB = <COD (CPCT)

thus, equal chords subtend equal angles at the centre.

Hope it helped you :)

Answer 2

Answer:

In triangle AOB and COD,

             OA = OC ( RADII OF THE SAME CIRCLE)

             OB = 0D  ( RADII OF THE SAME CIRCLE)

              AB = CD (GIVEN)

Therefore, Δ AOB ≅ Δ COD  

 This gives        ∠AOB = ∠COD (Corresponding parts of congruent triangle)