Two circles are congruent if they have the same radius

Asked by admin @ in Math viewed by 241 People

"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"

Answered by admin @


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

=========================================================

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....


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