Question

recall that two cicrels are congruent if they have the same radii.Prove that equal chords of congruent circles subtend equal angles at their centeres

Answer 1

Answer:

Let us consider a circle with center O and two equal chords of a circle AB and CD.

We need to prove that ∠AOB=∠COD

In △ AOB and COD, we have

AO=CO (Radius of the circle)

BO=DO (Radius of the circle)

AB=CD (Equal chords)

By SAS criterion of congruence, we have

△AOB≅△COD

⇒∠AOB=∠COD

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Answer 2

Given:-

• Chords are equal i.e AB = CD

To Prove:-

• $\rm{\angle{AOB} = \angle{COD}}$

Now,

In ∆AOB & ∆COD

→ AB = CD ( given)

→ AO = CO' ( equal radii )

→ BO = DO' ( equal radii )

So,

→ ∆ AOB ≈ ∆COD by S - S - S Congurency Criteria.

Therefore,

→ $\rm{\angle{AOB} = \angle{COD}}$ by C.P.C.T

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