Question

prove that if chords of congruent circles subtend equal angles at their centres .the the chords are equal?​

Answer 1

Given :

• ∠AOB = ∠COD

To Prove :

• AB = CD .

Solution :

Let a circle with centre O . AB and CD are two chords .

In Δ AOB and Δ COD :

$\longmapsto\tt{OA=OD\:(Radius)}$

$\longmapsto\tt{\angle{AOB}=\angle{COD}\:(Given)}$

$\longmapsto\tt{OB=OC\:(Radius)}$

So , By SAS Rule Δ AOB ≅ Δ COD ..

Now ,

$\longmapsto\tt{AB=CD\:(By\:CPCT\:Rule)}$

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Chord :

The line joining any two points on the circle is called as Chord .

Radius :

It is the distance from the centre of the circle to any point of the same circle .

CPCT :

CPCT stands for Corresponding Parts of Congruent Triangle .

SAS Rule :

Two triangles are congruent if two sides and the included angle of one triangle is equal to the sides and included angle of other Triangle .

_______________________

Answer 2

Given :

∠AOB = ∠COD

To Prove :

AB = CD .

Solution :

Let a circle with centre O . AB and CD are two chords .

In Δ AOB and Δ COD :

OA=OD (Radius)

<AOB = <COD (Given)

<OB = <OC (Radius)

So by SAS rule, ∆ AOB = ∆COD

Now,

AB = CD (By CPCT rule)

_______________________

Chord :

The line joining any two points on the circle is called as Chord .

Radius :

It is the distance from the centre of the circle to any point of the same circle .

CPCT :

CPCT stands for Corresponding Parts of Congruent Triangle .

SAS Rule :

Two triangles are congruent if two sides and the included angle of one triangle is equal to the sides and included angle of other Triangle .

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