Question

"Question 1 Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Class 9 - Math - Circles Page 173"

Answer 1

Two circles are said to be congruent if and only if their radii are equal.

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Let AB & CD  are two equal chords of two congruent circles with Centre O and O’. i.e AB= CD.

 

To Prove: ∠AOB = ∠CO'D

Proof:

In ΔAOB and ΔCO'D,

AB = CD ( given)

OA = O'C (Radii of congruent circles)

OB = O'D (Radii of congruent circles)

 ΔAOB ≅ ΔCO'D (SSS congruence rule)

 ∠AOB = ∠CO'D (By CPCT)

Hence, equal chords of congruent circles subtend equal angles at their centres.

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Hope this will help you....

Answer 2

Given;-

AB and CD r 2 equal chords of circle with centre ar O.

Proof:-
In ∆s AOB and COD ,we have

AO=CO

BO=DO

AB=CD.(GIVEN)


By SSS criteria of congruence,we have

∆AOB ~= ∆COD

angle AOB =angle COD (CPCT)

Hope it's help.